ORPP logo
Image from Google Jackets

Classical Artinian Rings And Related Topics.

By: Contributor(s): Material type: TextTextPublisher: Singapore : World Scientific Publishing Company, 2009Copyright date: ©2009Edition: 1st edDescription: 1 online resource (310 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9789814287258
Subject(s): Genre/Form: Additional physical formats: Print version:: Classical Artinian Rings And Related TopicsDDC classification:
  • 512
LOC classification:
  • QA251.3 -- .B325 2009eb
Online resources:
Contents:
Intro -- 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 -- 3.1 Definition of Harada Rings -- 3.2 A Dual Property of Harada Rings -- 3.3 The Relationships between Harada Rings and Co-Harada Rings -- COMMENTS -- 4. The Structure Theory of Left Harada Rings -- 4.1 Left Harada Rings of Types (]) and (¤) -- 4.2 A Construction of Left Harada Rings as Upper Staircase Factor Rings of Block Extensions of QF-Rings -- 4.3 The Representation of Left Harada Rings as Upper Staircase Factor Rings of Block Extensions of QF-Rings -- COMMENTS -- 5. Self-Duality of Left Harada Rings -- 5.1 Nakayama Isomorphisms, Weakly Symmetric Left H-Rings and Almost Self-Duality -- 5.2 Self-Duality and Almost Self-Duality of Left Harada Rings -- 5.3 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)-Type -- 7.5 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
No physical items for this record

Intro -- 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 -- 3.1 Definition of Harada Rings -- 3.2 A Dual Property of Harada Rings -- 3.3 The Relationships between Harada Rings and Co-Harada Rings -- COMMENTS -- 4. The Structure Theory of Left Harada Rings -- 4.1 Left Harada Rings of Types (]) and (¤) -- 4.2 A Construction of Left Harada Rings as Upper Staircase Factor Rings of Block Extensions of QF-Rings -- 4.3 The Representation of Left Harada Rings as Upper Staircase Factor Rings of Block Extensions of QF-Rings -- COMMENTS -- 5. Self-Duality of Left Harada Rings -- 5.1 Nakayama Isomorphisms, Weakly Symmetric Left H-Rings and Almost Self-Duality -- 5.2 Self-Duality and Almost Self-Duality of Left Harada Rings -- 5.3 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)-Type -- 7.5 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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.

© 2024 Resource Centre. All rights reserved.