S-Semiprime Submodules and S-Reduced Modules

Ayten Pekin, Ünsal Tekir, Özge Kılıç and Elena Guardo

Journal of Mathematics, 2020, vol. 2020, 1-7

Abstract: This article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity. Suppose that S is a multiplicatively closed subset of R. A submodule P of M is said to be an S-semiprime submodule if there exists a fixed s∈S, and whenever rnm∈P for some r∈R,m∈M, and n∈ℕ, then srm∈P. Also, M is said to be an S-reduced module if there exists (fixed) s∈S, and whenever rnm=0 for some r∈R,m∈M, and n∈ℕ, then srm=0. In addition, to give many examples and characterizations of S-semiprime submodules and S-reduced modules, we characterize a certain class of semiprime submodules and reduced modules in terms of these concepts.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8824787

DOI: 10.1155/2020/8824787

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