S. Loepp

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math.AC2025

Completions of Extremely Noncatenary Noetherian UFDs

Eli B. Dugan, S. Loepp

Let $T$ be a complete local ring. We present necessary and sufficient conditions for $T$ to be the completion of a local (Noetherian) unique factorization domain $A$ such that ther…

math.AC2025

Dimension-Preserving Saturated Embeddings of Finite Posets into the Spectra of Noetherian UFDs

David Baron, S. Loepp

Given a finite poset $X$ , we find necessary and sufficient conditions for there to exist a local Noetherian UFD $A$ and a saturated embedding of posets $Ï: X \longrightarrow \mbox…

math.AC2024

Constructing Noncatenary Quasi-Excellent Precompletions

Jackson Ehrenworth, S. Loepp

Let $T$ be a local (Noetherian) ring and let $Q_{1}$ and $Q_{2}$ be prime ideals of $T$ . We find sufficient conditions for there to exist a quasi-excellent local subring $B$ of $T$ sat…