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Gröbner bases in ring theory [[electronic resource] /] / Huishi Li
| Gröbner bases in ring theory [[electronic resource] /] / Huishi Li |
| Autore | Li Huishi |
| Pubbl/distr/stampa | Singapore, : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (295 p.) |
| Disciplina | 512.4 |
| Soggetto topico |
Gröbner bases
Rings (Algebra) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-4365-14-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 0. Introduction; 1. Preliminaries; 1.1 Presenting Algebras by Relations; 1.2 S-Graded Algebras and Modules; 1.3 -Filtered Algebras and Modules; 2. The -Leading Homogeneous Algebra A LH; 2.1 Recognizing A via G (A): Part 1; 2.2 Recognizing A via G (A): Part 2; 2.3 The -Graded Isomorphism A LH G (A); 2.4 Recognizing A via A LH; 3. Grobner Bases: Conception and Construction; 3.1 Monomial Ordering and Admissible System; 3.2 Division Algorithm and Grobner Basis; 3.3 Grobner Bases and Normal Elements; 3.4 Grobner Bases w.r.t. Skew Multiplicative K-Bases
3.5 Grobner Bases in KhX1, . . . ,Xni and KQ3.6 (De)homogenized Grobner Bases; 3.7 dh-Closed Homogeneous Grobner Bases; 4. Grobner Basis Theory Meets PBW Theory; 4.1 -Standard Basis and -PBW Isomorphism; 4.2 Realizing - PBW Isomorphism by Grobner Basis; 4.3 Classical PBW K-Bases vs Grobner Bases; 4.4 Solvable Polynomial Algebras Revisited; 5. Using AB LH in Terms of Grobner Bases; 5.1 The Working Strategy; 5.2 Ufnarovski Graph; 5.3 Determination of Gelfand-Kirillov Dimension; 5.4 Recognizing Noetherianity; 5.5 Recognizing (Semi-)Primeness and PI-Property 5.6 Anick's Resolution over Monomial Algebras5.7 Recognizing Finiteness of Global Dimension; 5.8 Determination of Hilbert Series; 6. Recognizing (Non-)Homogeneous p-Koszulity via ABLH; 6.1 (Non-)Homogeneous p-Koszul Algebras; 6.2 Anick's Resolution and Homogeneous p-Koszulity; 6.3 Working in Terms of Grobner Bases; 7. A Study of Rees Algebra by Grobner Bases; 7.1 Defining A by G*; 7.2 Defining A by G; 7.3 Recognizing Structural Properties of A via G; 7.4 An Application to Regular Central Extensions; 7.5 Algebras Defined by dh-Closed Homogeneous Grobner Bases; 8. Looking for More Grobner Bases 8.1 Lifting (Finite) Grobner Bases from On(λji)8.2 Lifting (Finite) Grobner Bases from a Class of Algebras; 8.3 New Examples of Grobner Basis Theory; 8.4 Skew 2-Nomial Algebras; 8.5 Almost Skew 2-Nomial Algebras; Bibliography; Index |
| Record Nr. | UNINA-9910457538003321 |
Li Huishi
|
||
| Singapore, : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gröbner bases in ring theory [[electronic resource] /] / Huishi Li
| Gröbner bases in ring theory [[electronic resource] /] / Huishi Li |
| Autore | Li Huishi |
| Pubbl/distr/stampa | Singapore, : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (295 p.) |
| Disciplina | 512.4 |
| Soggetto topico |
Gröbner bases
Rings (Algebra) |
| ISBN | 981-4365-14-9 |
| Classificazione | SK 230 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 0. Introduction; 1. Preliminaries; 1.1 Presenting Algebras by Relations; 1.2 S-Graded Algebras and Modules; 1.3 -Filtered Algebras and Modules; 2. The -Leading Homogeneous Algebra A LH; 2.1 Recognizing A via G (A): Part 1; 2.2 Recognizing A via G (A): Part 2; 2.3 The -Graded Isomorphism A LH G (A); 2.4 Recognizing A via A LH; 3. Grobner Bases: Conception and Construction; 3.1 Monomial Ordering and Admissible System; 3.2 Division Algorithm and Grobner Basis; 3.3 Grobner Bases and Normal Elements; 3.4 Grobner Bases w.r.t. Skew Multiplicative K-Bases
3.5 Grobner Bases in KhX1, . . . ,Xni and KQ3.6 (De)homogenized Grobner Bases; 3.7 dh-Closed Homogeneous Grobner Bases; 4. Grobner Basis Theory Meets PBW Theory; 4.1 -Standard Basis and -PBW Isomorphism; 4.2 Realizing - PBW Isomorphism by Grobner Basis; 4.3 Classical PBW K-Bases vs Grobner Bases; 4.4 Solvable Polynomial Algebras Revisited; 5. Using AB LH in Terms of Grobner Bases; 5.1 The Working Strategy; 5.2 Ufnarovski Graph; 5.3 Determination of Gelfand-Kirillov Dimension; 5.4 Recognizing Noetherianity; 5.5 Recognizing (Semi-)Primeness and PI-Property 5.6 Anick's Resolution over Monomial Algebras5.7 Recognizing Finiteness of Global Dimension; 5.8 Determination of Hilbert Series; 6. Recognizing (Non-)Homogeneous p-Koszulity via ABLH; 6.1 (Non-)Homogeneous p-Koszul Algebras; 6.2 Anick's Resolution and Homogeneous p-Koszulity; 6.3 Working in Terms of Grobner Bases; 7. A Study of Rees Algebra by Grobner Bases; 7.1 Defining A by G*; 7.2 Defining A by G; 7.3 Recognizing Structural Properties of A via G; 7.4 An Application to Regular Central Extensions; 7.5 Algebras Defined by dh-Closed Homogeneous Grobner Bases; 8. Looking for More Grobner Bases 8.1 Lifting (Finite) Grobner Bases from On(λji)8.2 Lifting (Finite) Grobner Bases from a Class of Algebras; 8.3 New Examples of Grobner Basis Theory; 8.4 Skew 2-Nomial Algebras; 8.5 Almost Skew 2-Nomial Algebras; Bibliography; Index |
| Record Nr. | UNINA-9910779074403321 |
|
Li Huishi
|
||
| Singapore, : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gröbner bases in ring theory [[electronic resource] /] / Huishi Li
| Gröbner bases in ring theory [[electronic resource] /] / Huishi Li |
| Autore | Li Huishi |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore, : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (295 p.) |
| Disciplina | 512.4 |
| Soggetto topico |
Gröbner bases
Rings (Algebra) |
| ISBN | 981-4365-14-9 |
| Classificazione | SK 230 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 0. Introduction; 1. Preliminaries; 1.1 Presenting Algebras by Relations; 1.2 S-Graded Algebras and Modules; 1.3 -Filtered Algebras and Modules; 2. The -Leading Homogeneous Algebra A LH; 2.1 Recognizing A via G (A): Part 1; 2.2 Recognizing A via G (A): Part 2; 2.3 The -Graded Isomorphism A LH G (A); 2.4 Recognizing A via A LH; 3. Grobner Bases: Conception and Construction; 3.1 Monomial Ordering and Admissible System; 3.2 Division Algorithm and Grobner Basis; 3.3 Grobner Bases and Normal Elements; 3.4 Grobner Bases w.r.t. Skew Multiplicative K-Bases
3.5 Grobner Bases in KhX1, . . . ,Xni and KQ3.6 (De)homogenized Grobner Bases; 3.7 dh-Closed Homogeneous Grobner Bases; 4. Grobner Basis Theory Meets PBW Theory; 4.1 -Standard Basis and -PBW Isomorphism; 4.2 Realizing - PBW Isomorphism by Grobner Basis; 4.3 Classical PBW K-Bases vs Grobner Bases; 4.4 Solvable Polynomial Algebras Revisited; 5. Using AB LH in Terms of Grobner Bases; 5.1 The Working Strategy; 5.2 Ufnarovski Graph; 5.3 Determination of Gelfand-Kirillov Dimension; 5.4 Recognizing Noetherianity; 5.5 Recognizing (Semi-)Primeness and PI-Property 5.6 Anick's Resolution over Monomial Algebras5.7 Recognizing Finiteness of Global Dimension; 5.8 Determination of Hilbert Series; 6. Recognizing (Non-)Homogeneous p-Koszulity via ABLH; 6.1 (Non-)Homogeneous p-Koszul Algebras; 6.2 Anick's Resolution and Homogeneous p-Koszulity; 6.3 Working in Terms of Grobner Bases; 7. A Study of Rees Algebra by Grobner Bases; 7.1 Defining A by G*; 7.2 Defining A by G; 7.3 Recognizing Structural Properties of A via G; 7.4 An Application to Regular Central Extensions; 7.5 Algebras Defined by dh-Closed Homogeneous Grobner Bases; 8. Looking for More Grobner Bases 8.1 Lifting (Finite) Grobner Bases from On(λji)8.2 Lifting (Finite) Grobner Bases from a Class of Algebras; 8.3 New Examples of Grobner Basis Theory; 8.4 Skew 2-Nomial Algebras; 8.5 Almost Skew 2-Nomial Algebras; Bibliography; Index |
| Record Nr. | UNINA-9910823873603321 |
|
Li Huishi
|
||
| Singapore, : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Noncommutative Gröbner Bases and Filtered-Graded Transfer [[electronic resource] /] / by Huishi Li
| Noncommutative Gröbner Bases and Filtered-Graded Transfer [[electronic resource] /] / by Huishi Li |
| Autore | Li Huishi |
| Edizione | [1st ed. 2002.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 |
| Descrizione fisica | 1 online resource (IX, 202 p.) |
| Disciplina | 512.4 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Associative rings
Rings (Algebra) Algorithms Associative Rings and Algebras |
| ISBN | 3-540-45765-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Chapter I: Basic Structural Tricks and Examples -- Chapter II: Gröbner Bases in Associative Algebras -- Chapter III: Gröbner Bases and Basic Algebraic-Algorithmic Structures -- Chapter IV: Filtered-Graded Transfer of Gröbner Bases -- Chapter V: GK-dimension of Modules over Quadric Solvable Polynomial Algebras and Elimination of Variables -- Chapter VI: Multiplicity Computation of Modules over Quadric Solvable Polynomial Algebras -- Chapter VII: (partial-)Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras -- Chapter VII: Regularity and Ko-group of Quadric Solvable Polynomial Algebras -- References -- Index. |
| Record Nr. | UNINA-9910144940903321 |
|
Li Huishi
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Noncommutative Gröbner Bases and Filtered-Graded Transfer [[electronic resource] /] / by Huishi Li
| Noncommutative Gröbner Bases and Filtered-Graded Transfer [[electronic resource] /] / by Huishi Li |
| Autore | Li Huishi |
| Edizione | [1st ed. 2002.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 |
| Descrizione fisica | 1 online resource (IX, 202 p.) |
| Disciplina | 512.4 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Associative rings
Rings (Algebra) Algorithms Associative Rings and Algebras |
| ISBN | 3-540-45765-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Chapter I: Basic Structural Tricks and Examples -- Chapter II: Gröbner Bases in Associative Algebras -- Chapter III: Gröbner Bases and Basic Algebraic-Algorithmic Structures -- Chapter IV: Filtered-Graded Transfer of Gröbner Bases -- Chapter V: GK-dimension of Modules over Quadric Solvable Polynomial Algebras and Elimination of Variables -- Chapter VI: Multiplicity Computation of Modules over Quadric Solvable Polynomial Algebras -- Chapter VII: (partial-)Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras -- Chapter VII: Regularity and Ko-group of Quadric Solvable Polynomial Algebras -- References -- Index. |
| Record Nr. | UNISA-996466618403316 |
|
Li Huishi
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||