Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493575 | Journal of Algebra | 2005 | 22 Pages |
Abstract
A right R-module M is non-singular if xIâ 0 for all non-zero xâM and all essential right ideals I of R. The module M is torsion-free if Tor1R(M,R/Rr)=0 for all râR. This paper shows that, for a ring R, the classes of torsion-free and non-singular right R-modules coincide if and only if R is a right Utumi-p.p.-ring with no infinite set of orthogonal idempotents. Several examples and applications of this result are presented. Special emphasis is given to the case where the maximal right ring of quotients of R is a perfect left localization of R.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ulrich Albrecht, John Dauns, Laszlo Fuchs,