SMALL MODULES OVER ABELIAN REGULAR RINGS

被引：0

作者：

Zemlicka, Jan ^{[1
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Prague 18675 8, Czech Republic

来源：

COMMUNICATIONS IN ALGEBRA | 2012年 / 40卷 / 07期

关键词：

Small modules; Von Neumann regular rings;

D O I：

10.1080/00927872.2011.580439

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2485 / 2493

页数：9