Products of idempotents in a quaternion ring

Dolžan, David (author)

Let $R$ be a finite commutative local principal ring, and let $H(R)$ denote the corresponding quaternion ring. We show that an element of $H(R)$ is a product of idempotents if and only if it can be expressed as a product of two idempotents. Moreover, we obtain an explicit formula for the number of elements of $H(R)$ admitting such a factorization.

• Language: English
• Keywords: finite rings, idempotent, quaternions, matrices
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 907–914
• Numbering: Vol. 76, no. 4
• PID: 20.500.12556/RUL-189475
• UDC: 512
• ISSN on article: 0139-9918
• DOI: 10.1515/ms-2025-1151
• COBISS.SI-ID: 271274243
• Publication date in RUL: 07.10.2026

Record is a part of a journal

• Title: Mathematica slovaca
• Shortened title: Math. slovaca
• Publisher: De Gruyter, De Gruyter Brill
• ISSN: 0139-9918
• COBISS.SI-ID: 27357184

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: končni kolobarji, idempotent, kvaternioni, matrike

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika