Centrally Essential Rings and Semirings

TL;DR

This paper reviews the concept of centrally essential rings and semirings, highlighting their properties, examples, and significance in algebraic structures, emphasizing their large and diverse class.

Contribution

It provides a comprehensive review of results related to centrally essential rings and semirings, including definitions, properties, and numerous examples, expanding understanding of their algebraic importance.

Findings

Centrally essential rings are either commutative or satisfy a specific centrality property.

The class of centrally essential rings is very large and diverse.

Many examples of such rings are provided in the work.

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