On commuting probability of finite rings II
  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. 
Parama Dutta and Rajat Kanti Nath
math.RA