Rings, Modules, and the Total

2004
ISBN: 978-3-7643-7125-8
Verlag: Springer

Buch, Englisch, 138 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 276 g

Reihe: Frontiers in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Mader, Adolf

Kasch, Friedrich

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

Preface.- General Background.- I. Fundamental Notions and Properties.- II. Good Conditions for the Total.- III. The Total of Modules with LE-decompositions.- IV. The Total in Torsion-Free Abelian Groups.- Bibliography.- Index.