On weakly 1-absorbing primary submodules

Abstract

In this paper, we introduce weakly 1-absorbing primary submodules of modules over commutative rings. Let [Formula: see text] be a commutative ring with a nonzero identity and [Formula: see text] be a nonzero unital module. A proper submodule [Formula: see text] of [Formula: see text] is said to be a weakly 1-absorbing primary submodule if whenever [Formula: see text] for some nonunit elements [Formula: see text] and [Formula: see text] then [Formula: see text] or [Formula: see text]-[Formula: see text] where [Formula: see text]-[Formula: see text] is the prime radical of [Formula: see text] 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.