TY - JOUR TT - Commuting probability for subrings and quotient rings AU - Buckley, Stephen M. AU - Machale, Desmond PY - 2017 DA - May DO - 10.13069/jacodesmath.284962 JF - Journal of Algebra Combinatorics Discrete Structures and Applications PB - iPeak Academy WT - DergiPark SN - 2148-838X SP - 189 EP - 196 VL - 4 IS - 2 (Special Issue: Noncommutative rings and their applications) KW - Commuting probability KW - Subring KW - Quotient ring N2 - We prove that the commuting probability of a finite ring is no larger thanthe commuting probabilities of its subrings and quotients, and characterizewhen equality occurs in such a comparison. CR - [1] S. M. Buckley, Distributive algebras, isoclinism, and invariant probabilities, Contemp. Math. 634 (2015) 31–52. CR - [2] S. M. Buckley, D. MacHale, Commuting probabilities of groups and rings, preprint. CR - [3] S. M. Buckley, D. MacHale, Á. Ní Shé, Finite rings with many commuting pairs of elements, preprint. CR - [4] J. D. Dixon, Probabilistic group theory, C. R. Math. Acad. Sci. Soc. R. Can. 24(1) (2002) 1–15. CR - [5] P. Erdös, P. Turán, On some problems of a statistical group–theory, IV, Acta Math. Acad. Sci. Hung. 19(3) (1968) 413–435. CR - [6] R. M. Guralnick, G. R. Robinson, On the commuting probability in finite groups, J. Algebra 300(2) (2006) 509–528. CR - [7] K. S. Joseph, Commutativity in non–abelian groups, PhD thesis, University of California, Los Angeles, 1969. CR - [8] D. MacHale, How commutative can a non–commutative group be? Math. Gaz. 58(405) (1974) 199–202. CR - [9] D. MacHale, Commutativity in finite rings, Amer. Math. Monthly 83(1) (1976) 30–32. CR - [10] D. Rusin, What is the probability that two elements of a finite group commute?, Pacific J. Math. 82(1) (1979) 237–247. UR - https://doi.org/10.13069/jacodesmath.284962 L1 - https://dergipark.org.tr/en/download/article-file/267255 ER -