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- Title
RINGS WHICH ADMIT FAITHFUL TORSION MODULES II.
- Authors
OMAN, GREG; SCHWIEBERT, RYAN; Gomez Pardo, J. L.
- 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.
- Subjects
RING theory; MODULES (Algebra); TORSION; ENDOMORPHISM rings; VALUATION theory; SEMISIMPLE Lie groups
- Publication
Journal of Algebra & Its Applications, 2012, Vol 11, Issue 3, p1250054-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498811005828