As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as 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.
Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined.
The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings.
Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest.

zlib/Mathematics/Michiel Hazewinkel, Nadiya Gubareni, V.V. Kirichenko/Algebras, Rings and Modules: Volume 2 (Mathematics and Its Applications)_747138.pdf

Algebras, Rings and Modules: Volume 2 (Mathematics and Its Applications Book 586)

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

Michiel Hazewinkel; Vladimir V. Kirichenko

Kluwer Academic Publishers

Springer; Kluwer

Mathematics and its applications (Kluwer Academic Publishers), v. 575, v. 586, Dordrecht, ©2004

Mathematics and its applications, v. 575, 586, Dordrecht, 2004-2007

United States, United States of America

1 edition, October 23, 2007

0

lg319956

{"edition":"1","isbns":["1402051409","1402051417","9781402051401","9781402051418"],"last_page":405,"publisher":"Springer","series":"Mathematics and Its Applications"}

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. 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. Includes Bibliographical References And Indexes.

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.

Mathematics and Its Applications
Erscheinungsdatum: 12.09.2007

2010-10-13