2024/02/26 by Alexandra Bonat, Bonat, Alexandra, S. Loepp +1
Mathematics · #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2402.16549
We demonstrate a class of local (Noetherian) unique factorization domains (UFDs) that are noncatenary at infinitely many places. In particular, if A is in our class of UFDs, then the prime spectrum of A contains infinitely many disjoint (except at the maximal ideal) noncatenary subsets. As a consequence of our result, there are infinitely many height one prime ideals P of A such that A/P is not catenary. We also construct a countable local UFD A satisfying the property that for every height one prime ideal P of A, A/P is not catenary.