Michiel Hazewinkel, Nadiya M. Gubareni

Algebras, Rings and Modules

Non-Commutative Algebras and Rings

• Gebundenes Buch

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: Apple Academic Press Inc.
• Seitenzahl: 388
• Erscheinungstermin: 26. Januar 2016
• Englisch
• Abmessung: 234mm x 157mm x 28mm
• Gewicht: 792g
• ISBN-13: 9781482245035
• ISBN-10: 1482245035
• Artikelnr.: 42472527

Autorenporträt

Michiel Hazewinkel, Nadiya M. Gubareni

Inhaltsangabe

Preface. Preliminaries. Basic general constructions of rings and modules.
Homological dimensions of rings and modules. Goldie and Krull dimensions of
rings and modules. Rings with Finiteness conditions.
Krull-Remak-Schmidt-Azumaya theorem. Hereditary and semihereditary rings.
Serial nonsingular rings. Jacobson's conjecture. Rings related to Finite
posets. Distributive and semidistributive rings. The group of extensions.
Modules over semiperfect rings. Representations of primitive posets.
Representations of quivers, species and finite dimensional algebras.
Artinian rings of finite representation type. Semiperfect rings of bounded
representation type.

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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)