Commuting probabilities of $n$-centralizer finite rings

Abstract

Let $R$ be a finite ring. The commuting probability of $R$, denoted by $\mathrm{Pr}(R)$, is the probability that any two randomly chosen elements of $R$ commute. $R$ is called an $n$-centralizer ring if it has $n$ distinct centralizers. In this paper, we compute $\mathrm{Pr}(R)$ for some $n$-centralizer finite rings.

9 pages