PI Artin--Schelter regular algebras of dimension 3 are unique factorization rings

arXiv (Cornell University) 2026 Preprint Open access

Read full text
Authors: Silu Liu, Quanshui Wu
DOI: 10.48550/arxiv.2602.14034
Cited by: 0

Abstract

We prove that all noetherian PI Artin--Schelter regular algebras of dimension $3$ are unique factorization rings. In a certain sense, this result is a noncommutative analogue to the fact that regular local rings of dimension 3 are UFDs. The fact constitutes a crucial component in the proof of the assertion that all regular local rings are UFDs, known as the Auslander--Buchsbaum theorem.

Fields of Study & Subjects

Rings Modules and Algebras Commutative Algebra and Its Applications Algebraic structures and combinatorial models

Publication details

Journal / source
arXiv (Cornell University)
Publication date
15 February 2026
Language
EN
Document type
Preprint