Small Modules over Abelian Regular Rings

Abstract

We study the structure of infinitely generated small modules over abelian regular rings, i.e., modules over which the covariant functor Hom commutes with direct sums. It is shown that every infinitely generated small module has either an infinitely generated factor which is at most 2^2ω -generated or a countably generated essential submodule. As a consequence, we prove a module-theoretic criterion of steadiness for abelian regular rings.

Key Words:

• Small modules
• Von Neumann regular rings

2000 Mathematics Subject Classification:

• 16D70
• 16E50

ACKNOWLEDGMENT

This work is part of the research project MSM 0021620839, financed by MŠMT.

Notes

Communicated by J. L. Gomez Pardo.