Year: 2026
Type: article
Abstract: In this paper we count the number of $k$ -potent elements over $\mathbb{H}_{\mathbb{Z}_{p}}$ ,where $\mathbb{H}_{\mathbb{Z}_{p}}$ is the quaternion algebra over $\mathbb{Z}_{p}$ , and we present a descriptive formula for thegeneral case. For $k\in \{3,4,5\}$ , we give an explicit formula forthese values. Moreover, as an application of these results, we count thenumber of solutions of the equation $x^{k}=1$ over $\mathbb{H}_{\mathbb{Z}_{p}}$. For this purpose, we will use computer as a toolto check and understand the behavior of these elements in all cases that will be studied.
Authors: Cristina Flaut, Andreea Baias
Institution: Ovidius University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7155174463