ENGLISH

Rings, Modules, and the Total

By Friedrich Kasch , Adolf Mader (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2004
ISBN
978-3-7643-7125-8, 978-3-7643-7801-1
DOI
10.1007/b96769
Language
english
Format
PDF
Filesize
1 MB (1099095 bytes)
Series
Frontiers in Mathematics
Edition
1
Pages
138\130
Orientation
yes
Scanned
yes
Time added
2013-08-20 22:02:31
Algebra; Associative Rings and Algebras; Group The

Description

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.

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