Michiel Hazewinkel, Nadiya Gubareni, V. V. Kirichenko

Algebras, Rings and Modules (eBook, PDF)

Volume 2

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 400
• Erscheinungstermin: 8. September 2007
• Englisch
• ISBN-13: 9781402051418
• Artikelnr.: 37355299

Autorenporträt

Michiel Hazewinkel, Nadiya M. Gubareni

Inhaltsangabe

Preliminaries.
Decompositions of rings.
Artinian and Noetherian rings.
Categories and functors.
Projectives, injectives and flats.
Homological dimensions.
Integral domains.
Dedekind domains.
Goldie rings.
Semiperfect rings.
Quivers of rings.
Serial rings and modules.
Serial rings and their properties.
Semiperfect semidistributive rings.

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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.

Rezensionen

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)