11 citations · 17 across the 15 of their papers we have counts for
15 papers
Products of Nilpotent and Idempotent Matrices over Finite Local Rings
David Dolžan
Let be a finite commutative local principal ring. We study products of nilpotent and idempotent matrices in . We show that every product of nilpotent and idempotent mat…
Eigenvalues of the product matrices of finite commutative rings
David Dolžan
The product matrix of a finite commutative ring and an element is the matrix , where if , and …
Products of nilpotents in a quaternion ring of odd order
David Dolžan
Let be a finite commutative local principal ring of cardinality , where for an odd prime and integer with . We determine the number…
Products of idempotents in a quaternion ring
David Dolžan
Let be a finite commutative local principal ring, and let denote the corresponding quaternion ring. We show that an element of is a product of idempotents if and…
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 is equal to some fixed element . We calculate this probability for semisimpl…
On the sumsets of exceptional units in quaternion rings
Hassan Cheraghpour, David Dolžan
We investigate sums of exceptional units in a quaternion ring over a finite commutative ring . We prove that in order to find the number of representations of an element…
The metric dimension of the total graph of a semiring
David Dolžan
We calculate the metric dimension of the total graph of a direct product of finite commutative antinegative semirings with their sets of zero-divisors closed under addition.
Semirings generated by idempotents
David Dolžan
We prove that a semiring multiplicatively generated by its idempotents is commutative and Boolean, if every idempotent in the semiring has an orthogonal complement. We prove that a…
The unitary Cayley graph of a semiring
David Dolžan
We study the unitary Cayley graph of a matrix semiring. We find bounds for its diameter, clique number and independence number, and determine its girth. We also find the relationsh…
The Wiener index and the Wiener Complexity of the zero-divisor graph of a ring
David Dolžan
We calculate the Wiener index of the zero-divisor graph of a finite semisimple ring. We also calculate the Wiener complexity of the zero-divisor graph of a finite simple ring and f…
The Metric Dimension of the Zero-Divisor Graph of a Matrix Semiring
David Dolžan
We determine the metric dimension of the zero-divisor graph of the matrix semiring over a commutative entire antinegative semiring.
Some multivariate imprecise shock model copulas
David Dolžan, Damjana Kokol Bukovšek, Matjaž Omladič +1
Bivariate imprecise copulas have recently attracted substantial attention. However, the multivariate case seems still to be a "blank slate". It is then natural that this idea be te…
The automorphism group of the zero-divisor digraph of matrices over an antiring
David Dolžan, Gabriel Verret
We determine the automorphism group of the zero-divisor digraph of the semiring of matrices over an antinegative commutative semiring with a finite number of zero-divisors.
The total graphs of finite rings
David Dolžan, Polona Oblak
In this paper we extend the study of total graphs to non-commutative finite rings . We prove that is connected if and only if is not local and we see that in t…
Diameters of commuting graphs of matrices over semirings
David Dolžan, Damjana Kokol Bukovšek, Polona Oblak
We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the…