On a Generalization of Lifting Modules via SSP-Modules

Talebi, Yahya; Hamzekolaee, Ali Reza Moniri

doi:10.1007/s41980-020-00520-4

Cited by 1 publication

(2 citation statements)

References 14 publications

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“…Example 3.6. [5] Let R = F [[x, y]] be the ring of formal power series over a field F in the indeterminates x and y. Then, R is a commutative noetherian local domain with maximal ideal J = Rx + Ry.…”

Section: Proofmentioning

confidence: 99%

“…Cofinitely supplemented modules were introduced by Alizade et al [1] and Smith [2]. Following these works, various generalizations of cofinitely supplemented modules, such as totally cofinitely supplemented [3], cofinitely weak supplemented [4], an H-cofinitely supplemented [5,6] and cofinitely weak rad-supplemented [7] were studied. The Goldie*-supplemented modules were introduced and characterized in [8,9].…”

Section: Introductionmentioning

confidence: 99%

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Cofinitely Goldie*-Supplemented Modules

GÜROĞLU

2023

Journal of New Theory

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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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Section: Proofmentioning

confidence: 99%