Abstract
Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be a unitary [Formula: see text]-module. By [Formula: see text] we denote the Jacobson radical of [Formula: see text]. The purpose of this paper is to introduce the concept of weakly [Formula: see text]-submodules generalizing [Formula: see text]-submodules. We call a proper submodule [Formula: see text] of [Formula: see text] a weakly [Formula: see text]-submodule if whenever [Formula: see text] for [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text] Various properties and characterizations of weakly [Formula: see text]-submodules are investigated especially in the case of multiplication modules.
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