20.500.12556/DiRROS-29422 Primes and absolutely or non-absolutely irreducible elements in atomic domains 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. absolutely irreducible elements non-absolutely irreducible elements non-unique factorization integer-valued polynomials irreducible elements transfer homomorphisms zero-sum sequences true false true Angleški jezik Ni določen Neznano 2026-05-18 12:33:15 2026-05-18 12:33:15 2026-05-19 03:54:40 0000-00-00 00:00:00 2026 0 0 str. 2631-2648 no. 6 Vol. 54 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 512:511 0092-7872 10.1080/00927872.2025.2586234 278487043 Primes_and_absolutely_or_non-absolutely_irreducible_elements_in_atomic_domains.pdf Primes_and_absolutely_or_non-absolutely_irreducible_elements_in_atomic_domains.pdf 1 FDE03EAEA7B5AE7CD577F915C75FE5E7 424b55881dc21f35a6883d41c4c0ecb133792c2c5d4263d3d52c5325e821fd43 4c4be173-52a5-11f1-8a5a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=44112 https://www.tandfonline.com/doi/full/10.1080/00927872.2025.2586234 1 fbf1373e-52a4-11f1-8a5a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=44111 Inštitut za matematiko, fiziko in mehaniko 0 0 0