Work

On the sumsets of exceptional units in quaternion rings

Year: 2025

Type: article

Abstract: We investigate sums of exceptional units in a quaternion ring H(R) over a finite commutative ring R. We prove that in order to find the number of representations of an element in H(R) as a sum of k exceptional units for some integer k ? 2, we can limit ourselves to studying the quaternion rings over local rings. For a local ring R of even order, we find the number of representations of an element of H(R) as a sum of k exceptional units for any integer k ? 2. For a local ring R of odd order, we find either the number or the bounds for the number of representations of an element of H(R) as a sum of 2 exceptional units.

Source: Filomat

DOI: 10.2298/fil2504301c

Authors: Hassan Cheraghpour, David Dolzan

Institutions: University of Primorska, University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Javna Agencija za Raziskovalno Dejavnost RS

Awards: Graph Theory in Preserver Problems, Algebra, operator theory and financial mathematics