Characterization of completions of noncatenary local domains and noncatenary local UFDs

Chloe I. Avery; Caitlyn Booms; Timothy M. Kostolansky; S. Loepp; Alex Semendinger

DOI:10.1016/J.JALGEBRA.2018.12.016
Corpus ID: 102338883

Characterization of completions of noncatenary local domains and noncatenary local UFDs

@article{Avery2017CharacterizationOC,
  title={Characterization of completions of noncatenary local domains and noncatenary local UFDs},
  author={Chloe I. Avery and Caitlyn Booms and Timothy M. Kostolansky and Susan Loepp and Alex Semendinger},
  journal={Journal of Algebra},
  year={2017}
}

Chloe I. AveryCaitlyn Booms Alex Semendinger
Published 12 September 2017
Mathematics, Economics
Journal of Algebra

6 Citations

Figures from this paper

Completions of countable excellent domains and countable noncatenary domains

S. LoeppTeresa Yu
Mathematics
2020

Completions of Uncountable Local Rings with Countable Spectra

S. LoeppTeresa Yu
Mathematics
Journal of Algebra
2021

We find necessary and sufficient conditions for a complete local (Noetherian) ring to be the completion of an uncountable local (Noetherian) domain with a countable spectrum. Our results suggest that…

Structure of spectra of precompletions

Erica BarrettEmil GrafS. LoeppK. StrongSharon Zhang
Mathematics
Rocky Mountain Journal of Mathematics
2020

Let T be a complete local (Noetherian) ring and let A be a local subring of T such that the completion of A with respect to its maximal ideal is T. We investigate the possible structures of the…

Every Finite Poset is Isomorphic to a Saturated Subset of the Spectrum of a Noetherian UFD

Cory H. ColbertS. Loepp
Mathematics
2022

. We show that every ﬁnite poset is isomorphic to a saturated subset of the spectrum of a Noetherian unique factorization domain. In addition, we show that every ﬁnite poset is isomorphic to a…

Maximal chains of prime ideals of different lengths in unique factorization domains

S. LoeppAlex Semendinger
Mathematics
Rocky Mountain Journal of Mathematics
2019

We show that, given integers $n_1,n_2, \ldots ,n_k$ with $2 < n_1 < n_2 < \cdots < n_k$, there exists a local (Noetherian) unique factorization domain that has maximal chains of prime ideals of…

Cardinalities of prime spectra of precompletions

Erica BarrettEmil GrafS. LoeppK. StrongSharon Zhang
Computer Science
Commutative Algebra
2021

Given a complete local (Noetherian) ring, necessary and sufficient conditions are found on the inline-formula content-type to allow for a local domain to exist such that there exists a localdomain of T.

References

SHOWING 1-10 OF 14 REFERENCES

SORT BY

Characterization of completions of unique factorization domains

R. Heitmann
Mathematics
1993

It is shown that a complete local ring is the completion of a unique factorization domain if and only if it is a field, a discrete valuation ring, or it has depth at least two and no element of its…

Constructing Local Generic Formal Fibers

S. Loepp
Mathematics
1997

Abstract Let ( T , M ) be a complete local (Noetherian) unique factorization domain of dimension at least two such that the cardinality of the residue field T / M is at least the cardinality of the…

Semilocal generic formal fibers

P. ChartersS. Loepp
Mathematics
2003

On the Chain Problem of Prime Ideals

M. Nagata
Mathematics
Nagoya Mathematical Journal
1956

There is a problem called the chain problem of prime ideals, which asks, when 0 is a Noetherian local integral domain, whether the length of an arbitrary maximal chain of prime ideals in 0 is equal…

Commutative Ring Theory

H. MatsumuraM. Reid
Mathematics
1989

Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7.…