On S-2-absorbing submodules and vn-regular modules

Abstract

Let R be a commutative ring and M an R-module. In this article, we introduce the concept of S-2-absorbing submodule. Suppose that S subset of R is a multiplicatively closed subset of R. A submodule P of M with (P :(R) M) boolean AND S = empty set is said to be an S-2-absorbing submodule if there exists an element s is an element of S and whenever abm is an element of P for some a, b is an element of R and m is an element of M, then sab is an element of (P :(R) M) or sam is an element of P or sbm is an element of P. Many examples, characterizations and properties of S-2-absorbing submodules are given. Moreover, we use them to characterize von Neumann regular modules in the sense [9].