Overview
- Accessible to anyone with a basic knowledge of ring and module theory
- A short introduction to torsion-free Abelian groups is included
Part of the book series: Frontiers in Mathematics (FM)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (5 chapters)
Keywords
About this book
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.
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Rings, Modules, and the Total
Authors: Friedrich Kasch, Adolf Mader
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/b96769
Publisher: Birkhäuser Basel
-
eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 2004
Softcover ISBN: 978-3-7643-7125-8Published: 25 June 2004
eBook ISBN: 978-3-7643-7801-1Published: 02 February 2005
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: X, 138
Number of Illustrations: 3 b/w illustrations
Topics: Algebra, Associative Rings and Algebras, Group Theory and Generalizations