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Ring Constructions and Applications.
This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more speciali...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific Publishing Company,
2001.
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| Colección: | Series in algebra.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface ; Chapter 1 Preliminaries ; 1.1 Groupoids ; 1.2 Groups ; 1.3 Semigroups ; 1.4 Rings ; Chapter 2 Graded Rings ; 2.1 Groupoid-Graded Rings ; 2.2 Semigroup-Graded Rings ; 2.3 Group-Graded Rings ; 2.4 Superalgebras ; Chapter 3 Examples of Ring Constructions.
- 3.1 Direct, Subdirect and Semidirect Products3.2 Group and Semigroup Rings, Monomial Rings ; 3.3 Crossed Products ; 3.4 Polynomial and Skew Polynomial Rings ; 3.5 Skew Group and Semigroup Rings ; 3.6 Twisted Group and Semigroup Rings ; 3.7 Power and Skew Power Series Rings ; 3.8 Edge and Path Algebras.
- 3.9 Matrix Rings and Generalized Matrix Rings 3.10 Triangular Matrix Representations ; 3.11 Morita Contexts ; 3.12 Rees Matrix Rings ; 3.13 Smash Products ; 3.14 Structural Matrix Rings ; 3.15 Incidence Algebras ; Chapter 4 The Jacobson Radical.
- 4.1 The Jacobson Radical of Groupoid-Graded Rings 4.2 Descriptions of the Jacobson Radical ; 4.3 Semisimple Semigroup-Graded Rings ; 4.4 Homogeneous Radicals ; 4.5 Radicals and Homogeneous Components ; 4.6 Nilness and Nilpotency ; Chapter 5 Groups of Units.
- Chapter 6 Finiteness Conditions 6.1 Groupoid-Graded Rings ; 6.2 Structural Approach of Jespers and Okininski; 6.3 Finiteness Conditions and Homogeneous Components ; 6.4 Classical Krull Dimension and Gabriel Dimension ; Chapter 7 PI-Rings and Varieties ; Chapter 8 Gradings of Matrix Rings.