Michiel Hazewinkel, Nadiya M. Gubareni

Algebras, Rings and Modules (eBook, PDF)

Non-commutative Algebras and Rings

• Format: PDF

Produktbeschreibung

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 388
• Erscheinungstermin: 5. April 2016
• Englisch
• ISBN-13: 9781482245059
• Artikelnr.: 44753996

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)