ON Z-SYMMETRIC MODULES

Articles in Press

Document Type : Original Manuscript

Authors

Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand.

Abstract

A ring $R$ is called a left $\mathcal{Z}$-symmetric ring if $ab \in \mathcal{Z}_l(R)$ implies $ba \in \mathcal{Z}_l(R)$, where $\mathcal{Z}_l(R)$ is the set of left zero-divisors. A right $\mathcal{Z}$-symmetric ring is defined similarly, and a $\mathcal{Z}$-symmetric ring is one that is both left and right $\mathcal{Z}$-symmetric. In this paper, we introduce the concept of $\mathcal{Z}$-symmetric modules as a generalization of $\mathcal{Z}$-symmetric ring. Additionally, we introduce the concept of an eversible module as an analogy to eversible rings and prove that every eversible module is also a $\mathcal{Z}$-symmetric module, like in the case of rings.

Keywords

References

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Journal of Algebraic Systems

Articles in Press, Accepted Manuscript
Available Online from 09 April 2024

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