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Fully S-coidempotent modules

    https://doi.org/10.1142/S0219498822502024Cited by:0 (Source: Crossref)

    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:MAnn2R(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.

    Communicated by S. R. López-Permouth

    AMSC: 13C13, 13A15