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.

zlib/Mathematics/Michiel Hazewinkel, Nadiya Gubareni, V.V. Kirichenko/Algebras, Rings and Modules: Volume 1 (Mathematics and Its Applications)_747166.pdf

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

Kluwer Academic Publishers

Mathematics and its applications -- v. 575, Mathematics and its applications (Kluwer Academic Publishers) -- v. 575., Dordrecht, London, Netherlands, 2004

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, December 20, 2004

2004, US, 2004

0

lg319968

{"edition":"1","isbns":["1402026900","9781402026904"],"last_page":392,"publisher":"Springer","series":"Mathematics and Its Applications"}

Includes bibliographical references and index.

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.

We assume the reader is familiar with basic concepts of abstract algebra such as semigroup, group.

Mathematics and Its Applications
Erscheinungsdatum: 01.10.2004

2010-10-13