2018/01/09 by Cory H. Colbert, Colbert, Cory H.
Mathematics · #13E05 (Primary) #Commutative Algebra (math.AC) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1801.02758
openalex publication_date 2018/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we develop a technique to "split" certain types of partially ordered sets into simpler ones and use that technique to give a partial answer to a conjecture by R. Wiegand and S. Wiegand on the structure of semi-local, two-dimensional Noetherian spectra in their exposition on Noetherian prime ideals. Specifically, we show that very many two-dimensional posets with finitely many height two nodes that satisfy the necessary conditions of being the spectrum of a Noetherian ring, along with a very mild cardinality assumption, are in fact the spectrum of a Noetherian ring.