English

The multiplication probability of a finite ring

Rings and Algebras 2025-04-18 v1

Abstract

We study the probability that the product of two randomly chosen elements in a finite ring RR is equal to some fixed element xRx \in R. We calculate this probability for semisimple rings and some special classes of local rings, and find the bounds for this probability for an arbitrary finite ring.

Keywords

Cite

@article{arxiv.2504.12886,
  title  = {The multiplication probability of a finite ring},
  author = {David Dolžan},
  journal= {arXiv preprint arXiv:2504.12886},
  year   = {2025}
}