Rings, modules and the total

Friedrich Kasch, Adolf Mader - Collection Frontiers in Mathematics

136 pages, parution le 09/07/2004

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Résumé

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.

Sommaire

General Background
Fundamental Notions and Properties
Good Conditions for the Total
The Total of Modules with LE-decompositions
The Total in Torsion-Free Abelian Groups

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Friedrich Kasch, Adolf Mader
Collection	Frontiers in Mathematics
Parution	09/07/2004
Nb. de pages	136
Format	17 x 24
Couverture	Broché
Poids	425g
Intérieur	Noir et Blanc
EAN13	9783764371258