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arXiv · 2602.14034

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

Silu Liu·Quanshui Wu
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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.

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Silu Liu, Quanshui Wu. 2026-02-25. PI Artin--Schelter regular algebras of dimension 3 are unique factorization rings. https://arxiv.org/abs/2602.14034

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