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arXiv · 2608.12642

The Noetherian Case of Bayart's Power-Series Question

Viet-Hoang Tran·Dung V. Nguyen·Quang X. Nguyen·Thieu N. Vo·Tan M. Nguyen
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Abstract

Let $R$ be a commutative Noetherian ring. We prove that if the one-variable formal power-series ring $R[[x]]$ is a unique factorization domain, then so is the two-variable formal power-series ring $R[[x,y]]$. This resolves a question raised by Bayart in 1973 for Noetherian coefficient rings. The proof uses the divisor theory of Noetherian normal domains, expressed through finite rank-one reflexive modules.

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Viet-Hoang Tran, Dung V. Nguyen, Quang X. Nguyen, Thieu N. Vo, Tan M. Nguyen. 2026-08-12. The Noetherian Case of Bayart's Power-Series Question. https://arxiv.org/abs/2608.12642

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