Are zero-symmetric simple nearrings with identity equiprime?

TL;DR

This paper demonstrates that zero-symmetric simple nearrings with identity can exist without being equiprime, resolving a long-standing open problem in algebra.

Contribution

It provides the first example of such nearrings, showing that the property of being equiprime does not necessarily hold.

Findings

Existence of zero-symmetric simple nearrings with identity that are not equiprime

Resolution of a longstanding open problem in nearring theory

Clarification of the relationship between simplicity and equiprimeness

Abstract

We show that there exist zero-symmetric simple nearrings with identity which are not equiprime, solving a longstanding open problem.