Abstract: The idea of regularity in algebraic structures was first introduced by J.C. Beidleman in 1968, followed by structural advancements made by Steve Ligh in 1970 in the context of regular near-rings. This paper explores several properties specific to regular near-rings, with an emphasis on their behavior in relation to their center, Boolean near-rings, and division near-rings. It is demonstrated that while both the center of a regular near-ring and Boolean near-rings themselves exhibit regularity, division near-rings do not conform to this property.
