On weakly 1 -absorbing primary submodules

Abstract

In this paper, we introduce weakly 1-absorbing primary submodules of modules over commutative rings. Let R be a commutative ring with a nonzero identity and M be a nonzero unital module. A proper submodule N of M is said to be a weakly 1-absorbing primary submodule if whenever 0≠abm N for some nonunit elements a,b R and m M, then ab (N: M) or m M-rad(N), where M-rad(N) is the prime radical of N. Many properties and characterizations of weakly 1-absorbing primary submodules are given. We also give the relations between weakly 1-absorbing primary submodules and other classical submodules such as weakly prime, weakly primary, weakly 2-absorbing primary submodules. Also, we use them to characterize simple modules. © 2024 World Scientific Publishing Company.