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math.RA2024
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…
math.RA2024
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.
math.RA2024
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…