Nil versions of prime submodules

چکیده مقاله

Let R be a commutative ring with identity and M be an R-module. A proper submodule P of M is said to be prime if for any r ∈ R and m ∈ M with rm ∈ P, we have m ∈ P or r ∈ (P:_RM). The aim of this paper is to introduce and investigate the notions of lopsided-nil-prime and lopsided-√Ann_R (M)-prime submodules of M as two generalizations of prime submodules of M. © 2026 World Scientific Publishing Company.