Regularity and Substructures of Hom

Language: English

Published by Birkhäuser, 2009

3764399899 / 9783764399894

Series: Book 12 of 48 - Frontiers in Mathematics

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Druck auf Anfrage Neuware - Printed after ordering - Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not nite-dimensional ([8, page 155], [32, page V]). Von Neumann proved ([32, Theorem 14. 1, page 208], [8, page 162]): Every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. The book of K. R. Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]). In abelian group theory the interest lay in determining those groups whose endomorphism rings were regular or had related properties ([11, Section 112], [29], [30], [12], [13], [24]). An interesting feature was introduced by Brown and McCoy ([4]) who showed that every ring contains a unique largest ideal, all of whose elements are regular elements of the ring. In all these studies it was clear that regularity was intimately related to direct sum decompositions. Ware and Zelmanowitz ([35], [37]) de ned regularity in modules and studied the structure of regular modules. Nicholson ([26]) generalized the notion and theory of regular modules. In this purely algebraic monograph we study a generalization of regularity to the homomorphism group of two modules which was introduced by the rst author ([19]). Little background is needed and the text is accessible to students with an exposure to standard modern algebra. In the following, Risaringwith1,and A, M are right unital R-modules.

Seller Inventory # 9783764399894

Title
Regularity and Substructures of Hom
Author
Adolf Mader
Publisher
Birkhäuser
Publication year
2009
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3764399899
ISBN 13
9783764399894
Item weight
326 grams
Dimensions
242x170x11 mm
Series
Book 12 of 48: Frontiers in Mathematics

AHA-BUCH GmbH

Einbeck, Germany

5-star seller

AbeBooks seller since August 14, 2006

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