On S-1-absorbing prime submodules

Abstract

Let [Formula: see text] be a commutative ring with non-zero identity, [Formula: see text] a multiplicatively closed subset of [Formula: see text] and [Formula: see text] a unital [Formula: see text]-module. In this paper, we introduce and study the concept of [Formula: see text]-1-absorbing prime submodules. A submodule [Formula: see text] of [Formula: see text] with [Formula: see text] is said to be [Formula: see text]-1-absorbing prime, if there exists an [Formula: see text] whenever [Formula: see text] for some non-unit elements [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text]. Some examples, characterizations and properties of [Formula: see text]-1-absorbing prime submodules are given. Moreover, we give some characterizations of [Formula: see text]-1-absorbing prime submodules in multiplication modules.