Cofinitely F-supplemented modules


Özdemir S.

Sao Paulo Journal of Mathematical Sciences, vol.18, pp.142-148, 2023 (ESCI)

Abstract

Let M be a module, and let U, V, F be submodules of M with F proper. We say
V is an F-supplement of U in M if it is minimal in the collection of submodules
F ⊆ X ⊆ M such that M = U + X . If every cofinite submodule of M has an (ample)
F-supplement, then we call M a (amply) cofinitely F-supplemented module. We give
some general properties of these modules, and we characterize them in terms of
their certain submodules.