The probability that the product of k elements in a finite ring is zero
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908405674803200 |
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| author | Sarma, Dibyasman Subedi, Tikaram |
| author_facet | Sarma, Dibyasman Subedi, Tikaram |
| contents | 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 $zp_{_k}(R)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_10392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The probability that the product of k elements in a finite ring is zero Sarma, Dibyasman Subedi, Tikaram Rings and Algebras 13M05, 13A99 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 $zp_{_k}(R)$. |
| title | The probability that the product of k elements in a finite ring is zero |
| topic | Rings and Algebras 13M05, 13A99 |
| url | https://arxiv.org/abs/2506.10392 |