Uniformly Primal Submodule over Noncommutative Ring

Lamis J. M. Abulebda and Andrei V. Kelarev

Journal of Mathematics, 2020, vol. 2020, 1-4

Abstract: Let R be an associative ring with identity and M be a unitary right R-module. A submodule N of M is called a uniformly primal submodule provided that the subset B of R is uniformly not right prime to N, if there exists an element s∈M−N with sRB⊆N.The set adjN=r∈R|mRr⊆N for some m∈M is uniformly not prime to N.This paper is concerned with the properties of uniformly primal submodules. Also, we generalize the prime avoidance theorem for modules over noncommutative rings to the uniformly primal avoidance theorem for modules.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1593253

DOI: 10.1155/2020/1593253

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