On ?-submodules and locally torsion free modules

Abstract

Aim of the present paper is to study ?-submodules of modules over commutative rings. Let M be a nonzero unital module over a commutative ring Ft having an identity 1 ? 0. A proper submodule TV of M is said to be a X-submodule if whenever am ? N for some a ? R and m? M, then ann(a) + (N : m) - R. Besides giving fundemantal properties of this new class of submodules, we characterize some important classes of rings and modules such as weak regular modules, von Neumann regular rings, locally torsion free modules, divisible modules, simple and torsion free modules in terms of our new concept. © 2024 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.