Algebras, rings and modules

Author(s)

• Hazewinkel, Michiel
• Gubareni, Nadiya
• Kirichenko, Vladimir V.

Bibliographic Information

Algebras, rings and modules

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

（Mathematics and its applications, v. 575 ; v. 586）

Kluwer Academic, c2004-

• v. 1 : hb
• v. 2 : hb
• e-book

Note

Vol. 1 includes bibliographical references (p. 365-368) and indexes; v .2 (hb) includes "Suggestions for further reading." (p. 385-387) and indexes

Vol. 2 (hb) published: Dordrecht : Springer, c2007

Description and Table of Contents

Volume

v. 1 : hb ISBN 9781402026904

Description

Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative"numbersystem". During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.

Table of Contents

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.

Volume

e-book ISBN 9781402051401

Description

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.

Table of Contents

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.

by "Nielsen BookData"

Details

• NCID: BA69189735
• ISBN:
  • 1402026900
  • 9781402051418
  • 9781402051401
• Country Code: ne
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Dordrecht
• Pages/Volumes: v.
• Size: 25 cm
• Parent Bibliography ID:
  • BA00044495