Some Properties of Cofinitely ⊕-G Modules

Abstract

In this work, cofinitely ⊕-g-supplemented modules are defined and some properties of these modules are investigated. It is proved that any direct sum of cofinitely ⊕-g-supplemented modules is also cofinitely ⊕-g-supplemented. Let M be a distributive and cofinitely ⊕-g-supplemented R-module. Then, every factor module and every homomorphic image of M are cofinitely ⊕-g-supplemented. Let M be a cofinitely ⊕-g-supplemented R-module with D3 property. Then, every cofinite direct summand of M is cofinitely ⊕-g-supplemented. Let M be an R-module with SSP property. Then, every cofinite essential submodule of M has a g-supplement that is a direct summand in M if and only if every essential maximal submodule of M has a g-supplement that is a direct summand in M. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.