Ring Characterizations with Mutually SS-Supplemented Modules

Year 2024, Volume: 13 Issue: 1, 30 - 34, 24.03.2024

Burcu Nişancı Türkmen , Zehra Betül Meşeci

https://doi.org/10.17798/bitlisfen.1310501

Abstract

In this text, the notion of mutually ss-supplemented modules characterizes 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 follows in the refinable modules, distributive modules, fully invariant submodules and (π-)projective modules. Especially it was proven that each 𝜋-projective mutually ss-supplemented module is amply mutually ss-supplemented. It was obtained that every ss-supplemented refinable module has direct summand which is a mutually ss-supplement in the module. It was shown that C=⨁_(ϱ∈Λ ) C_ϱ is a mutually ss-supplemented module which each submodule of C is a fully invariant submodule, for the family of mutually ss-supplemented modules {C_ϱ }_(ϱ∈Λ).

Keywords

Semisimple module, Mutual supplements, ss-supplement, Mutually ss-supplemented module

Rings Characterizations with Mutually SS-Supplemented Modules

Abstract

In this text, the notion of mutually ss-supplemented modules characterizes 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 follows in the refinable modules, distributive modules, fully invariant submodules and (π-)projective modules. Especially it was proven that each 𝜋-projective mutually ss-supplemented module is amply mutually ss-supplemented. It was obtained that every ss-supplemented refinable module has direct summand which is a mutually ss-supplement in the module. It was shown that C=⨁_(ϱ∈Λ ) C_ϱ is a mutually ss-supplemented module which each submodule of C is a fully invariant submodule, for the family of mutually ss-supplemented modules {C_ϱ }_(ϱ∈Λ).

Keywords

Semisimple modules, Mutually ss-supplemented modules, Mutual supplements, ss-supplement

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