- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 3
- Generalizations of prime submodules
Generalizations of prime submodules
Authors : S. Moradi, A. Azizi
Pages : 587-595
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Publication Date : 2015-06-01
Article Type : Research
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