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arXiv · 2506.10392

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

Dibyasman Sarma·Tikaram Subedi
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Abstract

In this paper, for a fixed integer $k\ge 2$, 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 $zp_{_k}(R)$.

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Dibyasman Sarma, Tikaram Subedi. 2025-06-12. The probability that the product of k elements in a finite ring is zero. https://arxiv.org/abs/2506.10392

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