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Cech cohomological dimensions for commutative rings / / David E. Dobbs
| Cech cohomological dimensions for commutative rings / / David E. Dobbs |
| Autore | Dobbs David E. |
| Edizione | [1st ed. 1970.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg : , : Springer-Verlag, , [1970] |
| Descrizione fisica | 1 online resource (VIII, 180 p.) |
| Disciplina | 510 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Dimension theory (Topology)
Homology theory Rings (Algebra) |
| ISBN | 3-540-36310-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cohomological dimension of fields -- On Cech dimension theories for rings -- A generalization of cohomological dimension for rings -- Number theoretic applications of a cech dimension theory. |
| Record Nr. | UNISA-996466652703316 |
Dobbs David E.
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| Berlin ; ; Heidelberg : , : Springer-Verlag, , [1970] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Classical and Quantum Physics : 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control / / edited by G. Marmo, David Martín de Diego, Miguel Muñoz Lecanda
| Classical and Quantum Physics : 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control / / edited by G. Marmo, David Martín de Diego, Miguel Muñoz Lecanda |
| Edizione | [1st ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (388 pages) |
| Disciplina | 530.15 |
| Collana | Springer Proceedings in Physics |
| Soggetto topico |
Teoria quàntica
Mathematical physics Calculus of variations Associative rings Rings (Algebra) Manifolds (Mathematics) Complex manifolds Differential geometry Theoretical, Mathematical and Computational Physics Mathematical Physics Calculus of Variations and Optimal Control; Optimization Associative Rings and Algebras Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-24748-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | List of speakers who confirmed their interest: -- Manuel Asorey (Universidad de Zaragoza, Spain) -- A.P. Balachandran (Syracuse University, New York, USA) -- Albero Saa (University of Campinas (UNICAMP), Brazil) -- José F. Cariñena (Universidad de Zaragoza, Spain) -- Fernando Falceto (Universidad de Zaragoza, Spain) -- J. Gracia-Bondía (Universidad de Zaragoza, Spain) -- José G. Llavona (Universidad Complutense de Madrid, Spain) -- Franco Magri (Università degli Studi di Milano-Bicocca, Italy) -- Giuseppe Marmo (Università di Napoli Federico II, Italy) -- Juan Carlos Marrero (Universidad de La Laguna, Spain) -- Juan Manuel Pérez-Pardo (Universidad Carlos III, Spain) -- Miguel A. Rodríguez (Universidad Complutense de Madrid, Spain) -- Fernando Lledó (Universidad Carlos II de Madrid, Spain) -- F. Lizzi (Università di Napoli Federico II, Italy) -- Antonio García (Universidad Carlos III de Madrid, Spain) -- Narciso Román Roy (Technical University of Catalonia , Spain) -- Patricia Vitale (Università di Napoli Federico II, Italy). |
| Record Nr. | UNINA-9910349503803321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Classical artinian rings and related topics [[electronic resource] /] / Yoshitomo Baba, Kiyoichi Oshiro
| Classical artinian rings and related topics [[electronic resource] /] / Yoshitomo Baba, Kiyoichi Oshiro |
| Autore | Baba Yoshitomo |
| Pubbl/distr/stampa | [Hackensack], N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (310 p.) |
| Disciplina | 512/.4 |
| Altri autori (Persone) | ŌshiroKiyoichi <1943-> |
| Soggetto topico |
Artin rings
Commutative rings Rings (Algebra) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-76146-3
9786612761461 981-4287-25-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; List of Symbols; 1. Preliminaries; 1.1 Background Sketch; 1.2 Semiperfect Rings and Perfect Rings; 1.3 Frobenius Algebras, and Nakayama Permutations and Nakayama Automorphisms of QF-Rings; 1.4 Notation in Matrix Representations of Rings; COMMENTS; 2. A Theorem of Fuller; 2.1 Improved Versions of Fuller's Theorem; 2.2 M-Simple-Injective and Quasi-Simple-Injective Modules; 2.3 Simple-Injectivity and the Condition r[e, g, f]; 2.4 ACC on Right Annihilator Ideals and the Condition r[e, g, f]; 2.5 Injectivity and Composition Length; COMMENTS; 3. Harada Rings
5.2 Self-Duality and Almost Self-Duality of Left Harada Rings5.3 Koike's Example of a QF-Ring without a Nakayama Automorphism; 5.4 Factor Rings of QF-Rings with a Nakayama Automorphism; COMMENTS; 6. Skew Matrix Rings; 6.1 Definition of a Skew Matrix Ring; 6.2 Nakayama Permutations vs Given Permutations; 6.3 QF-Rings with a Cyclic Nakayama Permutation; 6.4 Strongly QF-Rings; 6.5 Block Extensions of Skew Matrix Rings; COMMENTS; 7. The Structure of Nakayama Rings; 7.1 Kupisch Series and Kupisch Well-Indexed Set via Left HRings; 7.2 Nakayama QF-Rings; 7.3 A Classification of Nakayama Rings 7.4 An Example of a Nakayama QF-Ring of KNP(1 ! 1)-Type7.5 The Self-Duality of Nakayama Rings; COMMENTS; 8. Modules over Nakayama Rings; 8.1 Characterizations of Nakayama Rings by Lifting and Extending Properties; COMMENTS; 9. Nakayama Algebras; 9.1 Nakayama Algebras over Algebraically Closed Fields; 9.2 Nakayama Group Algebras; COMMENTS; 10. Local QF-rings; 10.1 Local QF-rings; 10.2 Examples of Local QF-Rings with Radical Cubed Zero; COMMENTS; Open Questions; Bibliography; Index |
| Record Nr. | UNINA-9910455611003321 |
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Baba Yoshitomo
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| [Hackensack], N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classical artinian rings and related topics [[electronic resource] /] / Yoshitomo Baba, Kiyoichi Oshiro
| Classical artinian rings and related topics [[electronic resource] /] / Yoshitomo Baba, Kiyoichi Oshiro |
| Autore | Baba Yoshitomo |
| Pubbl/distr/stampa | [Hackensack], N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (310 p.) |
| Disciplina | 512/.4 |
| Altri autori (Persone) | ŌshiroKiyoichi <1943-> |
| Soggetto topico |
Artin rings
Commutative rings Rings (Algebra) |
| ISBN |
1-282-76146-3
9786612761461 981-4287-25-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; List of Symbols; 1. Preliminaries; 1.1 Background Sketch; 1.2 Semiperfect Rings and Perfect Rings; 1.3 Frobenius Algebras, and Nakayama Permutations and Nakayama Automorphisms of QF-Rings; 1.4 Notation in Matrix Representations of Rings; COMMENTS; 2. A Theorem of Fuller; 2.1 Improved Versions of Fuller's Theorem; 2.2 M-Simple-Injective and Quasi-Simple-Injective Modules; 2.3 Simple-Injectivity and the Condition r[e, g, f]; 2.4 ACC on Right Annihilator Ideals and the Condition r[e, g, f]; 2.5 Injectivity and Composition Length; COMMENTS; 3. Harada Rings
5.2 Self-Duality and Almost Self-Duality of Left Harada Rings5.3 Koike's Example of a QF-Ring without a Nakayama Automorphism; 5.4 Factor Rings of QF-Rings with a Nakayama Automorphism; COMMENTS; 6. Skew Matrix Rings; 6.1 Definition of a Skew Matrix Ring; 6.2 Nakayama Permutations vs Given Permutations; 6.3 QF-Rings with a Cyclic Nakayama Permutation; 6.4 Strongly QF-Rings; 6.5 Block Extensions of Skew Matrix Rings; COMMENTS; 7. The Structure of Nakayama Rings; 7.1 Kupisch Series and Kupisch Well-Indexed Set via Left HRings; 7.2 Nakayama QF-Rings; 7.3 A Classification of Nakayama Rings 7.4 An Example of a Nakayama QF-Ring of KNP(1 ! 1)-Type7.5 The Self-Duality of Nakayama Rings; COMMENTS; 8. Modules over Nakayama Rings; 8.1 Characterizations of Nakayama Rings by Lifting and Extending Properties; COMMENTS; 9. Nakayama Algebras; 9.1 Nakayama Algebras over Algebraically Closed Fields; 9.2 Nakayama Group Algebras; COMMENTS; 10. Local QF-rings; 10.1 Local QF-rings; 10.2 Examples of Local QF-Rings with Radical Cubed Zero; COMMENTS; Open Questions; Bibliography; Index |
| Record Nr. | UNINA-9910780722803321 |
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Baba Yoshitomo
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| [Hackensack], N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classical artinian rings and related topics [[electronic resource] /] / Yoshitomo Baba, Kiyoichi Oshiro
| Classical artinian rings and related topics [[electronic resource] /] / Yoshitomo Baba, Kiyoichi Oshiro |
| Autore | Baba Yoshitomo |
| Pubbl/distr/stampa | [Hackensack], N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (310 p.) |
| Disciplina | 512/.4 |
| Altri autori (Persone) | ŌshiroKiyoichi <1943-> |
| Soggetto topico |
Artin rings
Commutative rings Rings (Algebra) |
| ISBN |
1-282-76146-3
9786612761461 981-4287-25-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; List of Symbols; 1. Preliminaries; 1.1 Background Sketch; 1.2 Semiperfect Rings and Perfect Rings; 1.3 Frobenius Algebras, and Nakayama Permutations and Nakayama Automorphisms of QF-Rings; 1.4 Notation in Matrix Representations of Rings; COMMENTS; 2. A Theorem of Fuller; 2.1 Improved Versions of Fuller's Theorem; 2.2 M-Simple-Injective and Quasi-Simple-Injective Modules; 2.3 Simple-Injectivity and the Condition r[e, g, f]; 2.4 ACC on Right Annihilator Ideals and the Condition r[e, g, f]; 2.5 Injectivity and Composition Length; COMMENTS; 3. Harada Rings
5.2 Self-Duality and Almost Self-Duality of Left Harada Rings5.3 Koike's Example of a QF-Ring without a Nakayama Automorphism; 5.4 Factor Rings of QF-Rings with a Nakayama Automorphism; COMMENTS; 6. Skew Matrix Rings; 6.1 Definition of a Skew Matrix Ring; 6.2 Nakayama Permutations vs Given Permutations; 6.3 QF-Rings with a Cyclic Nakayama Permutation; 6.4 Strongly QF-Rings; 6.5 Block Extensions of Skew Matrix Rings; COMMENTS; 7. The Structure of Nakayama Rings; 7.1 Kupisch Series and Kupisch Well-Indexed Set via Left HRings; 7.2 Nakayama QF-Rings; 7.3 A Classification of Nakayama Rings 7.4 An Example of a Nakayama QF-Ring of KNP(1 ! 1)-Type7.5 The Self-Duality of Nakayama Rings; COMMENTS; 8. Modules over Nakayama Rings; 8.1 Characterizations of Nakayama Rings by Lifting and Extending Properties; COMMENTS; 9. Nakayama Algebras; 9.1 Nakayama Algebras over Algebraically Closed Fields; 9.2 Nakayama Group Algebras; COMMENTS; 10. Local QF-rings; 10.1 Local QF-rings; 10.2 Examples of Local QF-Rings with Radical Cubed Zero; COMMENTS; Open Questions; Bibliography; Index |
| Record Nr. | UNINA-9910810530203321 |
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Baba Yoshitomo
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| [Hackensack], N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Clifford Algebras and Lie Theory / / by Eckhard Meinrenken
| Clifford Algebras and Lie Theory / / by Eckhard Meinrenken |
| Autore | Meinrenken Eckhard |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013 |
| Descrizione fisica | 1 online resource (321 p.) |
| Disciplina | 512.57 |
| Collana | Ergebnisse der Mathematik und ihrer Grezgebiete. |
| Soggetto topico |
Topological groups
Lie groups Associative rings Rings (Algebra) Mathematical physics Differential geometry Physics Topological Groups, Lie Groups Associative Rings and Algebras Mathematical Applications in the Physical Sciences Differential Geometry Mathematical Methods in Physics |
| ISBN | 3-642-36216-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Conventions -- List of Symbols -- 1 Symmetric bilinear forms -- 2 Clifford algebras -- 3 The spin representation -- 4 Covariant and contravariant spinors -- 5 Enveloping algebras -- 6 Weil algebras -- 7 Quantum Weil algebras -- 8 Applications to reductive Lie algebras -- 9 D(g; k) as a geometric Dirac operator -- 10 The Hopf–Koszul–Samelson Theorem -- 11 The Clifford algebra of a reductive Lie algebra -- A Graded and filtered super spaces -- B Reductive Lie algebras -- C Background on Lie groups -- References -- Index. |
| Record Nr. | UNINA-9910739481703321 |
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Meinrenken Eckhard
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| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Codes and rings : theory and practice / / Minjia Shi, Abel Alahmadi, Patrick Sole ; series editor Dominique Perrin
| Codes and rings : theory and practice / / Minjia Shi, Abel Alahmadi, Patrick Sole ; series editor Dominique Perrin |
| Autore | Shi Minjia |
| Pubbl/distr/stampa | London, England : , : Academic Press, , 2017 |
| Descrizione fisica | 1 online resource (320 pages) |
| Disciplina | 003.54 |
| Collana | Pure and Applied Mathematics |
| Soggetto topico |
Coding theory
Rings (Algebra) |
| ISBN | 0-12-813391-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910583483103321 |
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Shi Minjia
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| London, England : , : Academic Press, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé
| Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (201 p.) |
| Disciplina | 003/.54 |
| Altri autori (Persone) | SoléPatrick |
| Collana | Series on coding theory and cryptology |
| Soggetto topico |
Coding theory
Rings (Algebra) Quasi-Frobenius rings Number theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-75750-4
9786612757501 981-283-769-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; References; Partial Correlations of Sequences and Their Applications S. Bozta and P. Udaya; 1. Introduction and Background; 1.1. Outline of Paper; 2. Sequences and Correlations; 3. Rings, Trace Functions and Sequences; 3.1. Galois Ring Preliminaries; 3.2. Sequence Families- A, Band C; 4. The Partial Correlation and Its First Moment; 5. The Second Moment of the Partial Correlation Function; 6. Conclusions and Discussion; Acknowledgements; References; On the Structure of Cyclic and Negacyclic Codes over Finite Chain Rings H. Q. Dinh, S. R. Lopez-Per-mouth and S. Szabo
1. Introduction2. Chain Rings and Galois Rings; 3. Alternative Metrics for Codes over Finite Rings; 4. Constacyclic Codes over Arbitrary Commutative Finite Rings; 5. Simple-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 6. Repeated-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 7. Closing Remarks and A Few Generalizations; References; Linear Codes over Finite Chain Rings and Projective Hjelmslev Geometries T. Honold and 1. Landjev; 1. Introduction; 2. Modules over Finite Chain Rings; 2.1. Finite Chain Rings; 2.2. Structure of Finite Modules; 2.3. Free Modules 2.4. Counting Formulas3. Linear Codes over Finite Chain Rings; 3.1. Basic properties; 3.2. Code Spectra and Isomorphisms; 3.3. Mac Williams Identities; 4. Projective and Affine Hjelmslev Spaces; 4.1. Axiomatic Definition; 4.2. Coordinate Hjelmslev Geometries; 4.3. Multisets of Points in PHG(R~); 5. Linear Codes and Geometry; 5.1. Equivalence of Multisets of Points and Linear Codes; 5.2. Some Classes of Codes Defined Geometrically; 5.3. Generalized Gray Maps; 5.4. Linearly Representable Codes; 5.5. Homogeneous Weights and Strongly Regular Graphs; 6. Arcs in Projective Hjelmslev Planes 6.1. A General Upper Bound for the Size of an Arc6.2. Constructions for Arcs; 6.3. (k,2)-Arcs; 6.4. Dual Constructions; 6.5. Constructions Using Automorphisms; 6.6. Tables for Arcs in Geometries over Small Chain Rings; 7. Blocking Sets in Projective Hjelmslev Planes; 7.1. General Results; 7.2. Redei Type Blocking Sets; Acknowledgements; Bibliography; Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities 1. A. Wood; 1. Introduction; 2. Characters; 2.1. Basic results; 2.2. Additive form of characters; 2.3. Character modules 3. Finite rings3.1. Basic definitions; 3.2. Structure of finite rings; 3.3. Duality; 4. Mobius functions of posets; 4.1. Basic definitions; 4.2. Examples; 5. Linear codes over modules; sufficient conditions for the extension theorem; 5.1. Basic definitions; 5.2. The character module as alphabet: the case of Hamming weight; 5.3. Sufficient conditions: the case of Hamming weight; 5.4. Sufficient conditions: the case of rings; 5.5. Semi-linear transformations; 6. Necessary conditions for the extension theorem; 6.1. Statement of results; 6.2. Proof of Theorem 6.3 6.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditions |
| Record Nr. | UNINA-9910456143303321 |
| Singapore ; ; Hackensack, NJ, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé
| Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (201 p.) |
| Disciplina | 003/.54 |
| Altri autori (Persone) | SoléPatrick |
| Collana | Series on coding theory and cryptology |
| Soggetto topico |
Coding theory
Rings (Algebra) Quasi-Frobenius rings Number theory |
| ISBN |
1-282-75750-4
9786612757501 981-283-769-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; References; Partial Correlations of Sequences and Their Applications S. Bozta and P. Udaya; 1. Introduction and Background; 1.1. Outline of Paper; 2. Sequences and Correlations; 3. Rings, Trace Functions and Sequences; 3.1. Galois Ring Preliminaries; 3.2. Sequence Families- A, Band C; 4. The Partial Correlation and Its First Moment; 5. The Second Moment of the Partial Correlation Function; 6. Conclusions and Discussion; Acknowledgements; References; On the Structure of Cyclic and Negacyclic Codes over Finite Chain Rings H. Q. Dinh, S. R. Lopez-Per-mouth and S. Szabo
1. Introduction2. Chain Rings and Galois Rings; 3. Alternative Metrics for Codes over Finite Rings; 4. Constacyclic Codes over Arbitrary Commutative Finite Rings; 5. Simple-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 6. Repeated-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 7. Closing Remarks and A Few Generalizations; References; Linear Codes over Finite Chain Rings and Projective Hjelmslev Geometries T. Honold and 1. Landjev; 1. Introduction; 2. Modules over Finite Chain Rings; 2.1. Finite Chain Rings; 2.2. Structure of Finite Modules; 2.3. Free Modules 2.4. Counting Formulas3. Linear Codes over Finite Chain Rings; 3.1. Basic properties; 3.2. Code Spectra and Isomorphisms; 3.3. Mac Williams Identities; 4. Projective and Affine Hjelmslev Spaces; 4.1. Axiomatic Definition; 4.2. Coordinate Hjelmslev Geometries; 4.3. Multisets of Points in PHG(R~); 5. Linear Codes and Geometry; 5.1. Equivalence of Multisets of Points and Linear Codes; 5.2. Some Classes of Codes Defined Geometrically; 5.3. Generalized Gray Maps; 5.4. Linearly Representable Codes; 5.5. Homogeneous Weights and Strongly Regular Graphs; 6. Arcs in Projective Hjelmslev Planes 6.1. A General Upper Bound for the Size of an Arc6.2. Constructions for Arcs; 6.3. (k,2)-Arcs; 6.4. Dual Constructions; 6.5. Constructions Using Automorphisms; 6.6. Tables for Arcs in Geometries over Small Chain Rings; 7. Blocking Sets in Projective Hjelmslev Planes; 7.1. General Results; 7.2. Redei Type Blocking Sets; Acknowledgements; Bibliography; Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities 1. A. Wood; 1. Introduction; 2. Characters; 2.1. Basic results; 2.2. Additive form of characters; 2.3. Character modules 3. Finite rings3.1. Basic definitions; 3.2. Structure of finite rings; 3.3. Duality; 4. Mobius functions of posets; 4.1. Basic definitions; 4.2. Examples; 5. Linear codes over modules; sufficient conditions for the extension theorem; 5.1. Basic definitions; 5.2. The character module as alphabet: the case of Hamming weight; 5.3. Sufficient conditions: the case of Hamming weight; 5.4. Sufficient conditions: the case of rings; 5.5. Semi-linear transformations; 6. Necessary conditions for the extension theorem; 6.1. Statement of results; 6.2. Proof of Theorem 6.3 6.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditions |
| Record Nr. | UNINA-9910780728903321 |
| Singapore ; ; Hackensack, NJ, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé
| Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (201 p.) |
| Disciplina | 003/.54 |
| Altri autori (Persone) | SoléPatrick |
| Collana | Series on coding theory and cryptology |
| Soggetto topico |
Coding theory
Rings (Algebra) Quasi-Frobenius rings Number theory |
| ISBN |
1-282-75750-4
9786612757501 981-283-769-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; References; Partial Correlations of Sequences and Their Applications S. Bozta and P. Udaya; 1. Introduction and Background; 1.1. Outline of Paper; 2. Sequences and Correlations; 3. Rings, Trace Functions and Sequences; 3.1. Galois Ring Preliminaries; 3.2. Sequence Families- A, Band C; 4. The Partial Correlation and Its First Moment; 5. The Second Moment of the Partial Correlation Function; 6. Conclusions and Discussion; Acknowledgements; References; On the Structure of Cyclic and Negacyclic Codes over Finite Chain Rings H. Q. Dinh, S. R. Lopez-Per-mouth and S. Szabo
1. Introduction2. Chain Rings and Galois Rings; 3. Alternative Metrics for Codes over Finite Rings; 4. Constacyclic Codes over Arbitrary Commutative Finite Rings; 5. Simple-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 6. Repeated-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 7. Closing Remarks and A Few Generalizations; References; Linear Codes over Finite Chain Rings and Projective Hjelmslev Geometries T. Honold and 1. Landjev; 1. Introduction; 2. Modules over Finite Chain Rings; 2.1. Finite Chain Rings; 2.2. Structure of Finite Modules; 2.3. Free Modules 2.4. Counting Formulas3. Linear Codes over Finite Chain Rings; 3.1. Basic properties; 3.2. Code Spectra and Isomorphisms; 3.3. Mac Williams Identities; 4. Projective and Affine Hjelmslev Spaces; 4.1. Axiomatic Definition; 4.2. Coordinate Hjelmslev Geometries; 4.3. Multisets of Points in PHG(R~); 5. Linear Codes and Geometry; 5.1. Equivalence of Multisets of Points and Linear Codes; 5.2. Some Classes of Codes Defined Geometrically; 5.3. Generalized Gray Maps; 5.4. Linearly Representable Codes; 5.5. Homogeneous Weights and Strongly Regular Graphs; 6. Arcs in Projective Hjelmslev Planes 6.1. A General Upper Bound for the Size of an Arc6.2. Constructions for Arcs; 6.3. (k,2)-Arcs; 6.4. Dual Constructions; 6.5. Constructions Using Automorphisms; 6.6. Tables for Arcs in Geometries over Small Chain Rings; 7. Blocking Sets in Projective Hjelmslev Planes; 7.1. General Results; 7.2. Redei Type Blocking Sets; Acknowledgements; Bibliography; Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities 1. A. Wood; 1. Introduction; 2. Characters; 2.1. Basic results; 2.2. Additive form of characters; 2.3. Character modules 3. Finite rings3.1. Basic definitions; 3.2. Structure of finite rings; 3.3. Duality; 4. Mobius functions of posets; 4.1. Basic definitions; 4.2. Examples; 5. Linear codes over modules; sufficient conditions for the extension theorem; 5.1. Basic definitions; 5.2. The character module as alphabet: the case of Hamming weight; 5.3. Sufficient conditions: the case of Hamming weight; 5.4. Sufficient conditions: the case of rings; 5.5. Semi-linear transformations; 6. Necessary conditions for the extension theorem; 6.1. Statement of results; 6.2. Proof of Theorem 6.3 6.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditions |
| Record Nr. | UNINA-9910810533203321 |
| Singapore ; ; Hackensack, NJ, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Rings (Algebra)
(263)
- Associative rings (100)
- Associative Rings and Algebras (90)
- Group theory (48)
- Algebra (46)