| Title: | Primes and absolutely or non-absolutely irreducible elements in atomic domains |
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| Authors: | ID Fadinger, Victor (Author)
ID Frisch, Sophie (Author)
ID Nakato, Sarah (Author)
ID Smertnig, Daniel (Author)
ID Windisch, Daniel (Author) |
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| Files: |  PDF - Presentation file, download (1,71 MB)
MD5: FDE03EAEA7B5AE7CD577F915C75FE5E7
 URL - Source URL, visit https://www.tandfonline.com/doi/full/10.1080/00927872.2025.2586234
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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 give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or nonexistence of the following kinds of elements: (1) primes, (2) absolutely irreducible elements that are not prime, and (3) irreducible elements that are not absolutely irreducible. A nonzero non-unit is called absolutely irreducible (or, a strong atom) if every one of its powers factors uniquely into irreducibles. |
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| Keywords: | absolutely irreducible elements, non-absolutely irreducible elements, non-unique factorization, integer-valued polynomials, irreducible elements, transfer homomorphisms, zero-sum sequences |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 2631-2648 |
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| Numbering: | Vol. 54, no. 6 |
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| PID: | 20.500.12556/DiRROS-29422  |
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| UDC: | 512:511 |
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| ISSN on article: | 0092-7872 |
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| DOI: | 10.1080/00927872.2025.2586234 |
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| COBISS.SI-ID: | 278487043 |
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| Note: |
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| Publication date in DiRROS: | 18.05.2026 |
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| Views: | 28 |
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| Downloads: | 20 |
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| Metadata: |    |
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