2015/10/28 by Jutirekha Dutta, Dhiren Kumar Basnet, Dutta, Jutirekha +3
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research #Graph theory and applications #math.RA #msc:16U70 #msc:16U80
paper · pdf · doi:10.48550/arxiv.1510.08211
arxiv created 2015/10/28 · arxiv updated 2015/10/29
The commuting probability of a finite ring R, denoted by Pr(R), is the probability that any two randomly chosen elements of R commute. In this paper, we obtain several bounds for Pr(R) through a generalization of Pr(R). Further, we define \Z-isoclinism between two pairs of rings and show that the generalized commuting probability, defined in this paper, is invariant under \Z-isoclinism between two pairs of finite rings.