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Regularity and Substructures of Hom by Friedrich Kasch (English) Paperback Book

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Specificaties

Objectstaat
Nieuw: Een nieuw, ongelezen en ongebruikt boek in perfecte staat waarin geen bladzijden ontbreken of ...
ISBN-13
9783764399894
Book Title
Regularity and Substructures of Hom
ISBN
9783764399894
Series
Frontiers in Mathematics Ser.
Publication Year
2009
Type
Textbook
Format
Trade Paperback
Language
English
Publication Name
Regularity and Substructures of Hom
Author
Friedrich Kasch, Adolf Mader
Item Length
9.4in
Publisher
Springer Basel A&G
Item Width
6.7in
Item Weight
16 Oz
Number of Pages
Xv, 164 Pages

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Product Information

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

Product Identifiers

Publisher
Springer Basel A&G
ISBN-10
3764399899
ISBN-13
9783764399894
eBay Product ID (ePID)
71778463

Product Key Features

Author
Friedrich Kasch, Adolf Mader
Publication Name
Regularity and Substructures of Hom
Format
Trade Paperback
Language
English
Series
Frontiers in Mathematics Ser.
Publication Year
2009
Type
Textbook
Number of Pages
Xv, 164 Pages

Dimensions

Item Length
9.4in
Item Width
6.7in
Item Weight
16 Oz

Additional Product Features

Number of Volumes
1 Vol.
Lc Classification Number
Qa251.5
Reviews
From the reviews:This book is dedicated to generalizations of regularity for an Abelian group … . contains an excellent and detailed exposition of results on all types of regularity in Hom with consequences for modules and rings. It is accessible, with all necessary definitions and proofs, contains also a series of instructive examples. … interest both for students and specialists. (A. I. Kashu, Zentralblatt MATH, Vol. 1169, 2009), From the reviews: "This book is dedicated to generalizations of regularity for an Abelian group ... . contains an excellent and detailed exposition of results on all types of regularity in Hom with consequences for modules and rings. It is accessible, with all necessary definitions and proofs, contains also a series of instructive examples. ... interest both for students and specialists." (A. I. Kashu, Zentralblatt MATH, Vol. 1169, 2009)
Table of Content
Notation and Background.- Regular Homomorphisms.- Indecomposable Modules.- Regularity in Modules.- Regularity in HomR(A, M) as a One-sided Module.- Relative Regularity: U-Regularity and Semiregularity.- Reg(A, M) and Other Substructures of Hom.- Regularity in Homomorphism Groups of Abelian Groups.- Regularity in Categories.
Copyright Date
2009
Topic
Algebra / Abstract, Algebra / General
Dewey Decimal
512.42
Intended Audience
Scholarly & Professional
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics

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