On 2-absorbing primary submodules of modules over commutative ring with unity

Abstract

In this paper, we introduce the concept of a [Formula: see text]-absorbing primary submodule over a commutative ring with nonzero identity which is a generalization of primary submodule. Let [Formula: see text] be an [Formula: see text]-module and [Formula: see text] be a proper submodule of [Formula: see text]. Then [Formula: see text] is said to be a [Formula: see text]-absorbing primary submodule of [Formula: see text] if whenever [Formula: see text], [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text] or [Formula: see text]. We have given an example and proved number of results concerning [Formula: see text]-absorbing primary submodules. We have also proved the [Formula: see text]-absorbing primary avoidance theorem for submodules.