مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Information Journal Paper

Title

ON Z-SYMMETRIC MODULES

Pages

  119-131

Keywords

$\mathcal{Z}$-symmetric ring 
$\mathcal{Z}$-symmetric module 

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.

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