Algebras, rings and modules  v. 1 ~ e-book

by Michiel Hazewinkel, Nadiya Gubareni and V.V. Kirichenko

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.

「Nielsen BookData」より

The text of the first volume of the book covers the major topics in ring and module theory and includes both fundamental classical results and more recent developments. The basic tools of investigation are methods from the theory of modules, which allow a very simple and clear approach both to classical and new results. An unusual main feature of this book is the use of the technique of quivers for studying the structure of rings. A considerable part of the first volume of the book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistributive rings and tiled orders. Many results of this text until now have been available in journal articles only. This book is aimed at graduate and post-graduate students and for all mathematicians who use algebraic techniques in their work. This is a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and algebras and is suitable for independent study.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

この本の情報

書名 Algebras, rings and modules
著作者等 Gubareni, Nadiya
Hazewinkel, Michiel
Kirichenko, Vladimir V.
Kirichenko V. V. (Kiev Taras Shevchenko University)
シリーズ名 Mathematics and its applications
巻冊次 v. 1
v. 2
e-book
出版元 Kluwer Academic
刊行年月 c2004-
版表示 2 Rev ed
ページ数 v.
大きさ 25 cm
ISBN 1402026900
9781402051401
9781402051418
NCID BA69189735
※クリックでCiNii Booksを表示
言語 英語
出版国 オランダ
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