On relative commuting probability of finite rings
Parama Dutta, Rajat Kanti Nath
TL;DR
This paper investigates the probability that the commutator of a randomly chosen pair, with one element from a subring and the other from the entire finite ring, equals a specific element of the ring.
Contribution
It introduces a new probabilistic measure related to commutators in finite rings involving subrings, extending previous work on commuting probabilities.
Findings
Derived formulas for the probability of specific commutator values.
Analyzed how subring structure influences commutator probabilities.
Provided bounds and special cases for finite rings.
Abstract
In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself equals to a given element of the ring.
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