Algebras, Rings And Modules

This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers 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. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

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)