Algebras, Rings and Modules, Volume 2

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Springer Science & Business Media, Sep 8, 2007 - Mathematics - 400 pages
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As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras.

Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined.

The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings.

Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest.

 

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Contents

Quivers and their representations
53
Appendix to section 2 5 More about Dynkin and extended
105
Representations of posets and of finite dimensional
113
Frobenius algebras and quasiFrobenius rings
161
Right serial rings
219
Tiled orders over discrete valuation rings
255
Gorenstein matrices
327
Suggestions for further reading
385
Name index
397
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Page 3 - A subset H of a group G is a subgroup of G if and only if...
Page 10 - Theorem 1.4. (Lagrange's theorem). If G is a finite group and H is a subgroup of G. then the order of H divides the order of G.

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