# Rings, Modules, and the Total

- 11 Citations
- 1.2k Downloads

Part of the Frontiers in Mathematics book series (FM)

Advertisement

Book

- 11 Citations
- 1.2k Downloads

Part of the Frontiers in Mathematics book series (FM)

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.

Algebra Group Theory Modules Rings Abelian group algebra endomorphism ring Group theory homomorphism ring torsion

- DOI https://doi.org/10.1007/b96769
- Copyright Information Birkhäuser Basel 2004
- Publisher Name Birkhäuser Basel
- eBook Packages Springer Book Archive
- Print ISBN 978-3-7643-7125-8
- Online ISBN 978-3-7643-7801-1
- Series Print ISSN 1660-8046
- Series Online ISSN 1660-8054
- Buy this book on publisher's site