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(2 omega)-generated or a countably generated essential submodule.
As a consequence, we prove a module-theoretic criterion of steadiness for abelian regular rings.