# Eversible and reversible semigroups and semirings

## TL;DR

This paper explores properties of zero-divisors in semigroups and semirings, introduces prenearsemirings, and generalizes Cohn's theorem to reversible rings, also examining conditions for expectation semirings to be reversible or eversible.

## Contribution

It introduces prenearsemirings and extends Cohn's theorem to this new context, advancing understanding of reversibility in algebraic structures.

## Key findings

- Characterization of zero-divisors in semigroups and semirings
- Introduction of prenearsemirings as a new algebraic structure
- Generalization of Cohn's theorem for reversible rings

## Abstract

The main purpose of this paper is to investigate the zero-divisors of semigroups with zero and semirings and in particular, to discuss eversible and reversible semigroups and semirings. We also introduce a new ring-like algebraic structure called prenearsemiring and generalize Cohn's theorem for reversible rings in this context. Finally, we discuss when expectation semirings are reversible or eversible.