Fully S-coidempotent modules

چکیده مقاله

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and M be an R-module. A submodule N of M is called coidempotent if N = ((0:MAnnR2(N)). Also, M is called fully coidempotent if every submodule of M is coidempotent. In this paper, we introduce the concepts of S-coidempotent submodules and fully S-coidempotent R-modules as generalizations of coidempotent submodules and fully coidempotent R-modules. We explore some basic properties of these classes of R-modules. © 2022 World Scientific Publishing Company.