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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.
List of contents
Groups and group representations.- Quivers and their representations.- Representations of posets and of finite dimensional algebras.- Frobenius algebras and quasi-Frobenius rings.- Right serial rings.- Tiled orders over discrete valuation rings.- Gorenstein matrices.
Summary
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.
Additional text
From the reviews:
"This is the first of two volumes which aim to take the theory of associative rings and their modules from fundamental definitions to the research frontier. The book is written at a level intended to be accessible to students who have taken standard basic undergraduate courses in linear algebra and abstract algebra. … has been written with considerable attention to accuracy, and has been proofread with care. … A very welcome feature is the substantial set of bibliographic and historical notes at the end of each chapter." (Kenneth A. Brown, Mathematical Reviews, 2006a)
"The authors concentrate on the representation theory (of groups, algebras, posets …) and on the structure of some special rings. … The book is written on a level accessible to advanced students who have some experience with algebra. … Interesting historical comments and references close each chapter. A list of references for further reading is providing at the end of the book." (Stanislaw Kasjan, Mathematical Reviews, Issue 2009 b)
Report
From the reviews:
"This is the first of two volumes which aim to take the theory of associative rings and their modules from fundamental definitions to the research frontier. The book is written at a level intended to be accessible to students who have taken standard basic undergraduate courses in linear algebra and abstract algebra. ... has been written with considerable attention to accuracy, and has been proofread with care. ... A very welcome feature is the substantial set of bibliographic and historical notes at the end of each chapter." (Kenneth A. Brown, Mathematical Reviews, 2006a)
"The authors concentrate on the representation theory (of groups, algebras, posets ...) and on the structure of some special rings. ... The book is written on a level accessible to advanced students who have some experience with algebra. ... Interesting historical comments and references close each chapter. A list of references for further reading is providing at the end of the book." (Stanislaw Kasjan, Mathematical Reviews, Issue 2009 b)
