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Paper detail

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 non-existence 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 non-zero non-unit is called absolutely irreducible (or, a strong atom) if every one of its powers factors uniquely into irreducibles.

preprint2025arXivOpen access
Victor FadingerSophie FrischSarah NakatoDaniel SmertnigDaniel Windisch
math.AC
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Victor FadingerSophie FrischSarah NakatoDaniel SmertnigDaniel Windisch

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