Primes and absolutely or non-absolutely irreducible elements in atomic domainsFadinger, Victor (Avtor) Frisch, Sophie (Avtor) Nakato, Sarah (Avtor) Smertnig, Daniel (Avtor) Windisch, Daniel (Avtor) absolutely irreducible elementsnon-absolutely irreducible elementsnon-unique factorizationinteger-valued polynomialsirreducible elementstransfer homomorphismszero-sum sequencesWe 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.20262026-05-18 12:33:15Neznano29422sl