RINGS WHICH ADMIT FAITHFUL TORSION MODULES II

Abstract

Let R be an associative ring with identity. An (left) R-module M is said to be torsion if for every m ∈ M, there exists a nonzero r ∈ R such that rm = 0, and faithful provided rM = {0} implies r = 0 (r ∈ R). We call R (left) FT if R admits a nontrivial (left) faithful torsion module. In this paper, we continue the study of FT rings initiated in Oman and Schwiebert [Rings which admit faithful torsion modules, to appear in Commun. Algebra]. After presenting several examples, we consider the FT property within several well-studied classes of rings. In particular, we examine direct products of rings, Brown–McCoy semisimple rings, serial rings, and left nonsingular rings. Finally, we close the paper with a list of open problems.