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arXiv · 1510.08211

On commuting probability of finite rings

Jutirekha Dutta·Dhiren Kumar Basnet·Rajat Kanti Nath
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Abstract

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.

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Jutirekha Dutta, Dhiren Kumar Basnet, Rajat Kanti Nath. 2015-10-28. On commuting probability of finite rings. https://arxiv.org/abs/1510.08211

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