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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 |
Baba Yoshitomo
|
||
| [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 |
|
Baba Yoshitomo
|
||
| [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 |
|
Baba Yoshitomo
|
||
| [Hackensack], N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||