Cofinitely Goldie*-Supplemented Modules

Authors : Ayşe Tuğba GÜROĞLU

Pages : 35-42

Doi:10.53570/jnt.1260505

View : 38 | Download : 34

Publication Date : 2023-06-30

Article Type : Research Paper

Abstract :One of the generalizations of supplemented modules is the Goldie*-supplemented module, defined by Birkenmeier et al. using $\\beta^{\\ast}$ relation. In this work, we deal with the concept of the cofinitely Goldie*-supplemented modules as a version of Goldie*-supplemented module. A left $R$-module $M$ is called a cofinitely Goldie*-supplemented module if there is a supplement submodule $S$ of $M$ with $C\\beta^{\\ast}S$, for each cofinite submodule $C$ of $M$. Evidently, Goldie*-supplemented are cofinitely Goldie*-supplemented. Further, if $M$ is cofinitely Goldie*-supplemented, then $M/C$ is cofinitely Goldie*-supplemented, for any submodule $C$ of $M$. If $A$ and $B$ are cofinitely Goldie*-supplemented with $M=A\\oplus B$, then $M$ is cofinitely Goldie*-supplemented. Additionally, we investigate some properties of the cofinitely Goldie*-supplemented module and compare this module with supplemented and Goldie*-supplemented modules.
Keywords : Cofinitely supplemented module, Goldie supplemented module, cofinitely Goldie supplemented module