Translator Disclaimer
2020 Almost excellent unique factorization domains
Sarah M. Fleming, Susan Loepp
Involve 13(1): 165-180 (2020). DOI: 10.2140/involve.2020.13.165

Abstract

Let ( T , 𝔪 ) be a complete local (Noetherian) domain such that depth T > 1 . In addition, suppose T contains the rationals, | T | = | T 𝔪 | , and the set of all principal height-1 prime ideals of T has the same cardinality as T . We construct a universally catenary local unique factorization domain A such that the completion of A is T and such that there exist uncountably many height-1 prime ideals 𝔮 of A such that ( T ( 𝔮 A ) T ) 𝔮 is a field. Furthermore, in the case where T is a normal domain, we can make A “close” to excellent in the following sense: the formal fiber at every prime ideal of A of height not equal to 1 is geometrically regular, and uncountably many height-1 prime ideals of A have geometrically regular formal fibers.

Citation

Download Citation

Sarah M. Fleming. Susan Loepp. "Almost excellent unique factorization domains." Involve 13 (1) 165 - 180, 2020. https://doi.org/10.2140/involve.2020.13.165

Information

Received: 2 September 2019; Revised: 10 December 2019; Accepted: 10 December 2019; Published: 2020
First available in Project Euclid: 20 March 2020

zbMATH: 07172119
MathSciNet: MR4059949
Digital Object Identifier: 10.2140/involve.2020.13.165

Subjects:
Primary: 13F15, 13F40
Secondary: 13B35, 13J10

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.13 • No. 1 • 2020
MSP
Back to Top