On λ-submodules and locally torsion free modules
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Aim of the present paper is to study λ-submodules of modules over commutative rings. Let M be a nonzero unital module over a commutative ring R having an identity 1 ≠ 0. A proper submodule N of M is said to be a λ-submodule if whenever am ∈ N for some a ∈ R and m ∈ M, then ann(a) + (N : m) = R. Besides giving fundamental 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.
Abstract
Aim of the present paper is to study λ-submodules of modules over commutative rings. Let M be a nonzero unital module over a commutative ring R having an identity 1 ≠ 0. A proper submodule N of M is said to be a λ-submodule if whenever am ∈ N for some a ∈ R and m ∈ M, then ann(a) + (N : m) = R. Besides giving fundamental 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.
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