Rings Which Admit Faithful Torsion Modules

Abstract

Let R be a ring with identity, and let M be a unitary (left) R-module. Then M is said to be torsion provided that for every m ∈ M, there is a nonzero r ∈ R such that rm = 0. In this article, we study the question of the existence (and nonexistence) of faithful torsion modules over both commutative and noncommutative rings.

Key Words:

• Cofinality
• Faithful module
• FPF ring
• Quasi-Frobenius ring
• Regular cardinal
• Semiperfect ring
• Torsion module
• Valuation ring

2010 Mathematics Subject Classification:

• 16D10
• 13C05

Notes

Communicated by J. L. Gomez Pardo.