Adam Jones

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20182026

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math.AC2026

On Landweber`s unique factorization problem

Adam Jones, Elad Paran

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 for…

math.AC2023

Flat dimension for power series over valuation rings

Adam Jones

We examine the power series ring $R [[X]]$ over a valuation ring $R$ of rank 1, with proper, dense value group. We give a counterexample to Hilbert's syzygy theorem for $R [[X]]$ , i.…

math.AC2021

Skew power series rings over a prime base ring

Adam Jones, William Woods

In this paper, we investigate the structure of skew power series rings of the form $S = R [[x; σ, δ]]$ , where $R$ is a complete filtered ring and $(σ, δ)$ is a skew derivation respecti…