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2017 A generalization of the classof principally lifting modules
M. Hosseinpour, B. Ungor, Y. Talebi, A. Harmanci
Rocky Mountain J. Math. 47(5): 1539-1563 (2017). DOI: 10.1216/RMJ-2017-47-5-1539

Abstract

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module. In this paper, we introduce a class of modules which is analogous to that of Goldie$^*$-lifting and principally Goldie$^*$-lifting modules. The module~$M$ is called \textit {principally} $\mathcal {G}^*$-\nobreak $\delta $-\textit {lifting} if, for any $m\in M$, there exists a direct summand $N$ of $M$ such that $mR$ is $\beta ^*_{\delta }$-equivalent to $N$. We also introduce a generalization of Goldie$^*$-supplemented modules, namely, a module $M$ is said to be \textit {principally} $\mathcal {G}^*$-$\delta $-\textit {supplemented} if, for any $m\in M$, there exists a $\delta $-supplement~$N$ in~$M$ such that $mR$ is $\beta ^*_{\delta }$-equivalent to~$N$. We prove that some results of principally $\mathcal {G}^*$-lifting modules and Goldie$^*$-lifting modules can be extended to principally $\mathcal {G}^*$-\nobreak $\delta $-lifting modules for this general setting. Several properties of these modules are given, and it is shown that the class of principally $\mathcal {G}^*$-\nobreak $\delta $-lifting modules lies between the classes of principally $\delta $-lifting modules and principally $\mathcal {G}^*$-$\delta $-supplemented modules.

Citation

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M. Hosseinpour. B. Ungor. Y. Talebi. A. Harmanci. "A generalization of the classof principally lifting modules." Rocky Mountain J. Math. 47 (5) 1539 - 1563, 2017. https://doi.org/10.1216/RMJ-2017-47-5-1539

Information

Published: 2017
First available in Project Euclid: 22 September 2017

zbMATH: 1379.16001
MathSciNet: MR3705764
Digital Object Identifier: 10.1216/RMJ-2017-47-5-1539

Subjects:
Primary: 16D10, 16D70, 16D80

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 5 • 2017
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