- Sinop Üniversitesi Fen Bilimleri Dergisi
- Volume:9 Issue:1
- A Study On a New Generalization of $delta$-Supplemented Modules
A Study On a New Generalization of $delta$-Supplemented Modules
Authors : Emine Önal Kır
Pages : 114-127
Doi:10.33484/sinopfbd.1411952
View : 57 | Download : 48
Publication Date : 2024-06-29
Article Type : Research Paper
Abstract :For any ring $S$ and an $S$-module $W$, a submodule $G$ of $W$ is termed \\emph{co$_\\delta$-coatomic} if the quotient module $W/G$ is $\\delta$-coatomic. In this study, we introduce the term ($\\oplus$-)\\emph{co$_\\delta$-coatomically $\\delta$-supplemented module}, or shortly ($\\oplus$-)\\emph{co$_\\delta$-$\\delta$-supplemented module} to describe a module $W$ where each co$_\\delta$-coatomic submodule has a $\\delta$-supplement (that is a direct summand) in $W$. Furthermore, a module $W$ is identified as \\emph{co$_\\delta$-coatomically $\\delta$-semiperfect}, or shortly \\emph{co$_\\delta$-$\\delta$-semiperfect}, provided each $\\delta$-coatomic quotient module of $W$ has a projective $\\delta$-cover. It has been proved that over a $\\delta$-semiperfect ring $S$, the module $_{S}S$ is $\\oplus_{\\delta}$-co-coatomically supplemented if and only if $_{S}S$ is co$_\\delta$-$\\delta$-semiperfect if and only if $_{S}S$ is $\\oplus$-co$_\\delta$-$\\delta$-supplemented.Keywords : eş delta eşatom alt modül, eş delta eşatom delta tümlenmiş modül, oplus eş delta eşatom delta tümlenmiş modül, eş delta eşatom delta yarı mükemmel modül
ORIGINAL ARTICLE URL