on z-symmetric modules

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 ev ersible 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.