Centrally Essential Semirings

Abstract

A semiring is said to be centrally essential if for every non-zero element x, there exist two non-zero central elements y, z with xy = z. We give some examples of non-commutative centrally essential semirings and describe some properties of additively cancellative centrally essential semirings.The work of O.V. Lyubimtsev is done under the state assignment No 0729-2020-0055. A.A.Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013P.1.1. Example. We consider a semigroup (M, •) with multiplication table