Ring Characterizations with Mutually SS-Supplemented Modules

Abstract

In this text, the notion of mutually ss-supplemented modules is characterized with the help of semiperfect rings. For this, mutually ss-supplemented modules were first classified according to certain properties. These features can be listed as refinable modules, distributive modules, fully invariant submodules, and (𝜋�-) projective modules. It was determined that every submodule of an amply ss-supplemented module is mutually ss-supplemented. It was shown that 𝐶�=⨁𝜚�∈𝛬� 𝐶�𝜚� is a mutually ss-supplemented module in which each submodule of 𝐶� is a fully invariant submodule, for the family of mutually ss-supplemented modules {𝐶�𝜚�}𝜚�∈𝛬� .