Uniformly Primal Submodule over Noncommutative Ring

Abstract EN

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.