On the sum of an idempotent and a tripotent in a quaternion algebra over the ring of integers modulo p

Let H be denoted as quaternions. Quaternions form an algebra over a ring R, as an extension of complex numbers into a four dimensional space, where H = {a0 + a1i + a2j + a3k | a0, a1, a2, a3 ∈ R}. A quaternion algebra, particularly defined over fields of characteristic 0, finds numerous applications...

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Bibliographic Details
Published inITM Web of Conferences Vol. 67; p. 01022
Main Authors Lai, Wei Kit, Qua, Kiat Tat, Denis Chee Keong Wong
Format Conference Proceeding Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.01.2024
Subjects
Algebra
Complex numbers
Quaternions
Rings (mathematics)
Sums
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Summary:Let H be denoted as quaternions. Quaternions form an algebra over a ring R, as an extension of complex numbers into a four dimensional space, where H = {a0 + a1i + a2j + a3k | a0, a1, a2, a3 ∈ R}. A quaternion algebra, particularly defined over fields of characteristic 0, finds numerous applications in physics. In this article, we explore some properties of the sum of an idempotent and a tripotent in the finite ring H/Zp, adapting the definition of SIT rings that was introduced by Ying et al in 2016. We provide some conditions for H/Zp to be SIT rings and we give some examples of weakly tripotent rings (Breaz and Cimpean, 2018) in H/Zp.
ISSN:2431-7578
2271-2097
DOI:10.1051/itmconf/20246701022