On the sumsets of exceptional units in quaternion rings

Cheraghpour, Hassan (author), Dolžan, David (author)

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 $k \geq 2$‎, ‎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 $k \geq 2$‎. ‎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.

• Language: English
• Keywords: exceptional units, finite rings, quaternion rings
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2025
• Year: 2025
• Number of pages: Str. 1301-1310
• Numbering: Vol. 39, no. 4
• PID: 20.500.12556/RUL-176922
• UDC: 512
• ISSN on article: 0354-5180
• DOI: 10.2298/FIL2504301C
• COBISS.SI-ID: 229008387
• Publication date in RUL: 15.12.2025

Record is a part of a journal

• Title: Filomat
• Shortened title: Filomat
• Publisher: Department of Mathematics and Informatics, Faculty of Science and Mathematics, University of Niš
• ISSN: 0354-5180
• COBISS.SI-ID: 1024191828

Secondary language

• Language: Slovenian
• Keywords: izjemne enote, končni kolobarji, kvaternionski kolobarji

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: N1-0210
• Name: Uporaba grafov v problemih ohranjevalcev

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