Irreducible divisor pair domains
arXiv:1903.03870
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.
23 pages. v.2 slight editing throughout, prime-free characterization added and used throughout to simplify proofs, localization results added