Research Description

My primary research studies the prime ideal structure of Noetherian rings. Other interests include invariants of orders that arise from an algebraic context and order theory more generally.

Published Works

2023 A Structural Invariant On Certain Two-Dimensional Noetherian Partially Ordered Sets, Rocky Mountain Journal of Mathematics, Volume 53, No. 3, 711-724, DOI: 10.1216/rmj.2023.53.711

2022 (with S. Loepp) Gluing minimal prime ideals in local rings, Communications in Algebra, 51:1, 239-247, DOI: 10.1080/00927872.2022.2096226

2021 Enlarging localized polynomial rings while preserving their prime ideal structure, Journal of Algebra, Volume 575, Pages 14-30, 

2013 (with E. Burger, D. Clyde, G. Shin, and Z. Wang) Canonical Diophantine representations of natural numbers with respect to quadratic “bases.” J. Number Theory 133, no. 4, 1372-1388.

2012 (with E. Burger, D. Clyde, G. Shin, and Z. Wang) A generalization of a theorem of Lekkerkerker to Ostrowski’s decomposition of natural numbers. Acta Arith. 153 no. 3, 217-249.

Active Works

[Referee report received; currently in revisions] (with S. Loepp) Every finite poset is isomorphic to a saturated subset of the spectrum of some Noetherian UFD.

[Manuscript in production] (with A. Lee) Rigid-flexible values for embeddings of ellipsoids into almost-square polydisks.

New and Emerging Projects

Degree functions on Noetherian orders.

Counting antichains in inductive sequences of finite partial orders.

Other Works

On Two Dimensional Semi-Local Noetherian Spectra.

Current and Past Research Students

Troy Larsen
Eric Gazin
Alex Fedor