On commuting probability of finite rings II
Parama Dutta, Rajat Kanti Nath
TL;DR
This paper investigates the probability that the commutator of two elements from different subrings of a finite non-commutative ring equals a specific element, providing formulas, bounds, and characterizations.
Contribution
It introduces new formulas, bounds, and characterizations for the commuting probability in finite rings, extending previous work on ring commutativity probabilities.
Findings
Derived a computing formula for the probability
Established bounds on the commuting probability
Provided characterizations of specific cases
Abstract
The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different subrings of a finite non-commutative ring equals a given element of that ring. We obtain several results on this probability including a computing formula, some bounds and characterizations.
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Taxonomy
TopicsFinite Group Theory Research · Rings, Modules, and Algebras · Coding theory and cryptography