Regularity and Substructures of Hom

• Main Authors: Kasch, Friedrich (Author), Mader, Adolf (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2009.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Algebra.; Associative rings.; Rings (Algebra).; Group theory.; Associative Rings and Algebras.; Group Theory and Generalizations.

Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not ?nite-dimensional ([8, page 155], [32, page V]). Von Neumann proved ([32, Theorem 1...

Table of Contents:

• Notation and Background
• Regular Homomorphisms
• Indecomposable Modules
• Regularity in Modules
• Regularity in HomR(A, M) as a One-sided Module
• Relative Regularity: U-Regularity and Semiregularity
• Reg(A, M) and Other Substructures of Hom
• Regularity in Homomorphism Groups of Abelian Groups
• Regularity in Categories.