Rings, Modules, and the Total

Adolf Mader

ISBN 10: 3764371250 / ISBN 13: 9783764371258

Published by Birkhäuser Basel, Springer Basel Jun 2004, 2004

About this Item

Neuware -In a nutshell, the book deals with direct decompositions of modules and associated concepts. The central notion of 'partially invertible homomorphisms¿, namely those that are factors of a non-zero idempotent, is introduced in a very accessible fashion. Units and regular elements are partially invertible. The 'total¿ consists of all elements that are not partially invertible. The total contains the radical and the singular and cosingular submodules, but while the total is closed under right and left multiplication, it may not be closed under addition. Cases are discussed where the total is additively closed. The total is particularly suited to deal with the endomorphism ring of the direct sum of modules that all have local endomorphism rings and is applied in this case. Further applications are given for torsion-free Abelian groups.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 152 pp. Englisch.

Seller Inventory # 9783764371258

Bibliographic Details

• Title: Rings, Modules, and the Total
• Publisher: Birkhäuser Basel, Springer Basel Jun 2004
• Publication Date: 2004
• Language: English
• ISBN 10: 3764371250
• ISBN 13: 9783764371258
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 170H x 9D millimeters 244 millimeters width by 170 millimeters height by 9 millimeters depth
• Weight: 276 grams

About this title

Synopsis

In a nutshell, the book deals with direct decompositions of modules and associated concepts. The central notion of "partially invertible homomorphisms”, namely those that are factors of a non-zero idempotent, is introduced in a very accessible fashion. Units and regular elements are partially invertible. The "total” consists of all elements that are not partially invertible. The total contains the radical and the singular and cosingular submodules, but while the total is closed under right and left multiplication, it may not be closed under addition. Cases are discussed where the total is additively closed. The total is particularly suited to deal with the endomorphism ring of the direct sum of modules that all have local endomorphism rings and is applied in this case. Further applications are given for torsion-free Abelian groups.

Review

From the reviews:

“The book is self-contained, well organized and nicely written, making it a very effective introduction to the subject at hand: the total.” (MAA REVIEWS)