Fully S-coidempotent modules

Abstract

Let [Formula: see text] be a commutative ring with identity, [Formula: see text] be a multiplicatively closed subset of [Formula: see text], and [Formula: see text] be an [Formula: see text]-module. A submodule [Formula: see text] of [Formula: see text] is called coidempotent if [Formula: see text]. Also, [Formula: see text] is called fully coidempotent if every submodule of [Formula: see text] is coidempotent. In this paper, we introduce the concepts of [Formula: see text]-coidempotent submodules and fully [Formula: see text]-coidempotent [Formula: see text]-modules as generalizations of coidempotent submodules and fully coidempotent [Formula: see text]-modules. We explore some basic properties of these classes of [Formula: see text]-modules.