Paul J. Truman

activity

20102026

most citedTowards a Generalisation of Noether's Theorem to Nonclassical Hopf-Galois Structures

5 citations · 17 across the 14 of their papers we have counts for

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9 papers · 1 filter

math.NT2022

On $ρ$ -conjugate Hopf-Galois structures

Paul J. Truman

The Hopf-Galois structures admitted by a Galois extension of fields $L / K$ with Galois group $G$ correspond bijectively with certain subgroups of $Perm (G)$ . We use a…

math.NT2019

Hopf-Galois module structure of tamely ramified radical extensions of prime degree

Paul J Truman

Let $K$ be a number field and let $L / K$ be a tamely ramified radical extension of prime degree $p$ . If $K$ contains a primitive $p^{t h}$ root of unity then $L / K$ is a c…

math.NT2017

Isomorphism problems for Hopf-Galois structures on separable field extensions

Alan Koch, Timothy Kohl, Paul J. Truman +1

Let $L / K$ be a finite separable extension of fields whose Galois closure $E / K$ has group $G$ . Greither and Pareigis have used Galois descent to show that a Hopf algebra givin…

math.NT2017

Normality and Short Exact Sequences of Hopf-Galois Structures

Alan Koch, Timothy Kohl, Paul J. Truman +1

Every Hopf-Galois structure on a finite Galois extension $K / k$ where $G = G a l (K / k)$ corresponds uniquely to a regular subgroup $N \leq B = Perm (G)$ , normalized by $λ(G)\l…

math.NT2017★ 4 cited

The Structure of Hopf Algebras Acting on Dihedral Extensions

Alan Koch, Timothy Kohl, Paul J. Truman +1

We discuss isomorphism questions concerning the Hopf algebras that yield Hopf-Galois structures for a fixed separable field extension $L / K$ . We study in detail the case where $L / K$ …

math.NT2017

Commutative Hopf-Galois module structure of tame extensions

Paul J. Truman

We prove three theorems concerning the Hopf-Galois module structure of fractional ideals in a finite tamely ramified extension of $p$ -adic fields or number fields which is $H$ -…

math.NT2016

Commuting Hopf-Galois Structures on a Separable Extension

Paul J. Truman

Let $L / K$ be a finite separable extension of local or global fields in any characteristic, let $H_{1}, H_{2}$ be two Hopf algebras giving Hopf-Galois structures on the extensio…

math.NT2014

Canonical Nonclassical Hopf-Galois Module Structure of Nonabelian Galois Extensions

Paul J Truman

Let $L / K$ be a finite Galois extension of local or global fields in characteristic $0$ or $p$ with nonabelian Galois group $G$ , and let $B$ be a $G$ -stable fractional i…

math.NT2010★ 5 cited

Towards a Generalisation of Noether's Theorem to Nonclassical Hopf-Galois Structures

Paul J. Truman

We study the nonclassical Hopf-Galois module structure of rings of algebraic integers in some extensions of $p$ -adic fields and number fields which are at most tamely ramified. W…

On ρ-conjugate Hopf-Galois structures

Hopf-Galois module structure of tamely ramified radical extensions of prime degree

Isomorphism problems for Hopf-Galois structures on separable field extensions

Normality and Short Exact Sequences of Hopf-Galois Structures

The Structure of Hopf Algebras Acting on Dihedral Extensions

Commutative Hopf-Galois module structure of tame extensions

Commuting Hopf-Galois Structures on a Separable Extension

Canonical Nonclassical Hopf-Galois Module Structure of Nonabelian Galois Extensions

Towards a Generalisation of Noether's Theorem to Nonclassical Hopf-Galois Structures

On $ρ$ -conjugate Hopf-Galois structures