The Noetherian Case of Bayart's Power-Series Question
Viet-Hoang Tran, Dung V. Nguyen, Quang X. Nguyen, Thieu N. Vo, Tan M. Nguyen
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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