David Dolžan

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20192026

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3 papers · 1 filter

math.RA2026

Eigenvalues of the product matrices of finite commutative rings

David Dolžan

The product matrix of a finite commutative ring $R = {x_{1}, x_{2}, \dots, x_{n}}$ and an element $u \in R$ is the matrix $A_{u} (R) = [a_{ij}]$ , where $a_{ij} = 1$ if $x_{i} x_{j} = u$ , and $a_{ij} = 0$ …

math.RA2025

Products of nilpotents in a quaternion ring of odd order

David Dolžan

Let $R$ be a finite commutative local principal ring of cardinality $q^{n}$ , where $q = p^{r}$ for an odd prime $p$ and integer $r$ with $R / J (R) ≃ GF (q)$ . We determine the number…

math.RA2025

The multiplication probability of a finite ring

David Dolžan

We study the probability that the product of two randomly chosen elements in a finite ring $R$ is equal to some fixed element $x \in R$ . We calculate this probability for semisimpl…