Finite Posets as Prime Spectra of Commutative Noetherian Rings

Authors

David T. Alkass, Mälardalen UniversityFollow

Abstract

We study finite partially ordered sets of prime ideals as found in commutative Noetherian rings. In doing so, we establish that these posets have a bipartite structure and devise a construction for finding ring spectra that are order-isomorphic to many such posets. Specifically, we prove that any finite complete bipartite graph is order-isomorphic to the spectrum of a ring of essentially finite type over the field of rational numbers. Furthermore, we prove that prime spectra of such rings can also depict any finite path or even cycle.

Author Bio

David Alkass is a student of Mathematics from Sweden. This paper was written as an extension of his Bachelor thesis. He looks forward to attending graduate school with the aim of making meaningful contributions to the field of mathematics in the future.

Faculty Sponsor

Peder Thompson

Recommended Citation

Alkass, David T. (2024) "Finite Posets as Prime Spectra of Commutative Noetherian Rings," Rose-Hulman Undergraduate Mathematics Journal: Vol. 25: Iss. 2, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol25/iss2/7