S. Loepp

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20232025

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6 papers · 1 filter

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 $ϕ: 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…

math.AC2024

Noncatenary Unique Factorization Domains

Alexandra Bonat, S. Loepp

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…

math.AC2024

Noncatenary splinters in prime characteristic

S. Loepp, Austyn Simpson

We construct a local Noetherian splinter (in fact, a weakly $F$ -regular domain) in prime characteristic which is not catenary, which we view as an analogue of a theorem of Ogoma in…

math.AC2023

Controlling Formal Fibers of Countably Many Principal Prime Ideals

David Baron, Ammar Eltigani, S. Loepp +2

Let $T$ be a complete local (Noetherian) ring. For each $i \in N$ , let $C_{i}$ be a nonempty countable set of nonmaximal pairwise incomparable prime ideals of $T$ , and suppo…