The multiplication probability of a finite ring

2025/04/17 by David Dolžan, Dolžan, David
Computer Science · Mathematics · #Coding theory and cryptography #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2504.12886

openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the probability that the product of two randomly chosen elements in a finite ring R is equal to some fixed element x ∈ 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.

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