ON Z-SYMMETRIC MODULES

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.

کلیدواژه ها:

\mathcal{Z}-symmetric ring ، \mathcal{Z}-symmetric module ، eversible ring ، eversible module