# 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} }

## 6 Citations

### Completions of Uncountable Local Rings with Countable Spectra

- MathematicsJournal 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

- MathematicsRocky 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

- 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

- MathematicsRocky 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

- Computer ScienceCommutative 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.

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