Centrally Essential Rings and Semirings

Abstract

This work is a review of results about centrally essential rings and semirings. A ring (resp., semiring) is said to be centrally essential if it is either commutative or satisfy the property that for any non-central element $a$, there exist non-zero central elements $x$ and $y$ with $ax=y$. The class of centrally essential rings is very large; many corresponding examples are given in the work