Algebras, rings and modules
著者
書誌事項
Algebras, rings and modules
（Mathematics and its applications, v. 575 ; v. 586）
Kluwer Academic, c2004-
- v. 1 : hb
- v. 2 : hb
- e-book
大学図書館所蔵 件 / 全24件
-
v. 1 : hb411.7//H49//166015100212347,15100212925,15100216603,
v. 2 : hb411.7//H49//438815100243888 -
該当する所蔵館はありません
- すべての絞り込み条件を解除する
この図書・雑誌をさがす
注記
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
内容説明・目次
- 巻冊次
-
v. 1 : hb ISBN 9781402026904
内容説明
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.
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.
- 巻冊次
-
e-book ISBN 9781402051401
内容説明
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.
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