Generalizations of prime submodules

Abstract

Let R be a commutative ring with identity and M a unitary R-module, and n > 1 an integer number. As a generalization of the concept of prime submodules, a proper submodule N of M will be called n-almost prime, if for r ∈ R and x ∈ M with rx ∈ N \ (N : M) n−1N, either x ∈ N or r ∈ (N : M). We study n-almost prime submodules, in this paper.

Keywords

• Essential multiplicatively closed subsets; n-almost prime submodules; Prime submodules

References

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