PI Artin--Schelter regular algebras of dimension 3 are unique factorization rings
Rings and Algebras
2026-02-26 v2
Abstract
We prove that all noetherian PI Artin--Schelter regular algebras of dimension 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.
Keywords
Cite
@article{arxiv.2602.14034,
title = {PI Artin--Schelter regular algebras of dimension 3 are unique factorization rings},
author = {Silu Liu and Quanshui Wu},
journal= {arXiv preprint arXiv:2602.14034},
year = {2026}
}