Primes and absolutely or non-absolutely irreducible elements in atomic domains
Abstract
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.
Fields of Study & Subjects
History and advancements in chemistry
Graph theory and applications
Publication details
- Journal / source
- Communications in Algebra
- Publisher
- Informa UK Limited
- Volume
- 54
- Issue
- 6
- Pages
- 2631–2648
- Publication date
- 8 January 2026
- Language
- EN