English

Irreducible divisor pair domains

Commutative Algebra 2019-09-04 v2

Abstract

We introduce and study a new class of integral domains which we call irreducible divisor pair domains (IDPDs). In particular, we show how IDPDs fit in with other classes of integral domains defined in terms of factorization conditions. For instance, every UFD is an IDPD, and every IDPD is an HFD, but the converses fail in general. We also show that many familiar examples of HFDs are also IDPDs.

Cite

@article{arxiv.1903.03870,
  title  = {Irreducible divisor pair domains},
  author = {Sean K. Sather-Wagstaff},
  journal= {arXiv preprint arXiv:1903.03870},
  year   = {2019}
}

Comments

23 pages. v.2 slight editing throughout, prime-free characterization added and used throughout to simplify proofs, localization results added

R2 v1 2026-06-23T08:03:11.205Z