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arXiv · 2607.03475

On Landweber`s unique factorization problem

Adam Jones·Elad Paran
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Abstract

We solve a long-standing open problem, posed by Landweber in 1974: Let $R = K[x_1, x_2, . . . ]$ be the ring of polynomials in countably many variables over a field $K$. Is the formal power series ring $R[[t]]$ a unique factorization domain? We prove that it is. The proof is based on a new general result in commutative algebra: If $R$ is a Krull domain, and $f \in R[[t]]$ is irreducible, then $f$ is irreducible modulo a finite power of $t$.

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Adam Jones, Elad Paran. 2026-07-03. On Landweber`s unique factorization problem. https://arxiv.org/abs/2607.03475

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