Generalizations of prime submodules

Authors : S. MORADİ, A. AZİZİ

Pages : 587-595

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Publication Date : 2015-06-01

Article Type : Research Paper

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 \ insert ignore into journalissuearticles values(N : M); n−1N, either x ∈ N or r ∈ insert ignore into journalissuearticles values(N : M);. We study n-almost prime submodules, in this paper.
Keywords : Essential multiplicatively closed subsets, n almost prime submodules, Prime submodules