Adam Jones

activity

20182026

collaborators

9 papers

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.RT2026

New directions in the study of prime ideals in rational, nilpotent Iwasawa algebras

Adam Jones, William Woods

Let G be a nilpotent p-valuable (compact p-adic Lie) group. There is an ongoing investigation into the prime ideals of its completed group algebra (Iwasawa algebra), and there rema…

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.RA2023

Filtered skew derivations on simple artinian rings

Adam Jones, William Woods

Given a complete, positively filtered ring $(R, f)$ and a compatible skew derivation $(σ, δ)$ , we may construct its skew power series ring $R [[x; σ, δ]]$ . Due to topological obstructio…

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…

math.RT2021

Primitive ideals in rational, nilpotent Iwasawa algebras

Adam Jones

Given a $p$ -adic field $K$ and a nilpotent uniform pro- $p$ group $G$ , we prove that all primitive ideals in the $K$ -rational Iwasawa algebra $K G$ are maximal, and can be reduced to…

math.RT2021

Affinoid Dixmier modules and the deformed Dixmier-Moeglin equivalence

Adam Jones

The affinoid envelope, $U (L)$ of a free, finitely generated $Z_{p}$ -Lie algebra $L$ has proven to be useful within the representation theory of…

math.GR2019

A Control Theorem for Primitive ideals in Iwasawa algebras

Adam Jones

Let p be a prime, K a p-adic field, G a nilpotent, uniform pro-p group. We prove that all faithful, primitive ideals in the Iwasawa algebra KG are controlled by the centraliser of…

math.RT2018

Completed Group Algebras of Abelian-by-procyclic Groups

Adam Jones

Let p be a prime, let G be a p-valuable, abelian-by-procyclic group, and let k be a field of characteristic p. We will prove that all faithful prime ideals of the completed group a…