What question did this study set out to answer?

The aim is to define Z-symmetric modules and explore their relationship with Z-symmetric rings and eversible modules.

June 14, 2026Open Access

On Z-Symmetric Modules

Key Points

The aim is to define Z-symmetric modules and explore their relationship with Z-symmetric rings and eversible modules.
Introduced the concept of Z-symmetric modules as an extension of Z-symmetric rings.
Defined eversible modules and established their connection to Z-symmetric modules through theoretical proofs.
Proved that every eversible module is also a Z-symmetric module, similar to eversible rings.

Abstract

A ring R is called a left Z-symmetric ring if ab Zₗ (R) implies ba Zₗ (R), where Zₗ (R) is the set of left zero-divisors. A right Z-symmetric ring is defined similarly, and a Z-symmetric ring is one that is both left and right Z-symmetric. In this paper, we introduce the concept of Z-symmetric modules as a generalization of 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 Z-symmetric module, like in the case of rings.

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