Primes and absolutely or non-absolutely irreducible elements in atomic domains
Commutative Algebra
2026-01-13 v2
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.
Keywords
Cite
@article{arxiv.2411.01051,
title = {Primes and absolutely or non-absolutely irreducible elements in atomic domains},
author = {Victor Fadinger and Sophie Frisch and Sarah Nakato and Daniel Smertnig and Daniel Windisch},
journal= {arXiv preprint arXiv:2411.01051},
year = {2026}
}
Comments
24 pages, to appear in Comm. Algebra