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Frontiers in Mathematics

Rings, Modules, and the Total

Authors: Kasch, Friedrich, Mader, Adolf

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  • ISBN 978-3-7643-7801-1
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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)


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • The eBook version of this title will be available soon
  • ISBN 978-3-7643-7801-1
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-7643-7125-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Rings, Modules, and the Total
Authors
Series Title
Frontiers in Mathematics
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-7643-7801-1
DOI
10.1007/b96769
Softcover ISBN
978-3-7643-7125-8
Series ISSN
1660-8046
Edition Number
1
Number of Pages
X, 138
Number of Illustrations
3 b/w illustrations
Topics