| Title: | On the sumsets of exceptional units in quaternion rings |
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| Authors: | ID Cheraghpour, Hassan (Author)
ID Dolžan, David (Author) |
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| Files: |  PDF - Presentation file, download (221,05 KB)
MD5: 03461C489E185E34BF339146649D273C
 URL - Source URL, visit https://doiserbia.nb.rs/Article.aspx?ID=0354-51802504301C
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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 $k \geq 2$, 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. |
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| Keywords: | exceptional units, finite rings, quaternion rings |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1301-1310 |
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| Numbering: | Vol. 39, no. 4 |
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| PID: | 20.500.12556/DiRROS-24715  |
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| UDC: | 512 |
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| ISSN on article: | 0354-5180 |
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| DOI: | 10.2298/FIL2504301C |
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| COBISS.SI-ID: | 229008387 |
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| Publication date in DiRROS: | 15.12.2025 |
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| Views: | 7 |
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| Downloads: | 5 |
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