The probability that the product of k elements in a finite ring is zero

2025/06/12 by Sarma, Dibyasman, Subedi, Tikaram
#13A99 #13M05 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2506.10392

Abstract

In this paper, for a fixed integer k≥ 2, we study the probability that the product of k randomly chosen elements in a finite commutative ring R is zero, which we denote by zp_k(R). We investigate bounds for zp_k(R) that turn out to be sharp bounds for certain classes of rings. Further, we determine the maximum value of zp_k(R) that can be obtained for any ring R, and classify all rings within some specific range of zp_k(R).

Citations

• An Algebraic Identity Leading to Wilson Theorem
• On some problems of a statistical group-theory. IV

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