Weakly Tripotent Elements in Quaternion Rings over ℤp

Abstract

Let R be a ring. An element x ∈ R is weakly tripotent if x can be written as x3 = x or x3 = −x. In this paper, we discuss weakly tripotency in quaternion rings over ℤp, ℍ/ℤp. We also give some conditions for the element x ∈ ℍ/ℤp to be weakly tripotent.