Generalizations of prime submodules

Year 2015, Volume: 44 Issue: 3, 587 - 595, 01.06.2015

S. Moradi A. Azizi

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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