Cofinitely Goldie*-Supplemented Modules
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 $M$...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Naim Çağman
2023-06-01
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| Series: | Journal of New Theory |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/2991186 |
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| Summary: | 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. |
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| ISSN: | 2149-1402 |