L. Childs

activity

20132023

most citedBi-skew braces and Hopf Galois structures

23 citations · 26 across the 8 of their papers we have counts for

collaborators

9 papers

math.RA2023

On the Galois correspondence ratio for Hopf-Galois extensions arising from nilpotent $F_{p}$ -algebras

Lindsay N. Childs

For a Hopf-Galois structure on a Galois extension $L / K$ of fields that arises from a finite nilpotent $F_{p}$ -algebra $A$ , we look at the Galois correspondence ratio, which…

math.RA2022

Skew left braces and the Yang-Baxter equation

Lindsay N. Childs

We give a self-contained proof that a skew left brace yields a solution of the Yang-Baxter equation.

math.RA2019

On the Galois correspondence for Hopf Galois structures arising from finite radical algebras and Zappa-Szép products

Lindsay N. Childs

Let $L / K$ be a $G$ -Galois extension of fields with an $H$ -Hopf Galois structure of type $N$ . We study the ratio $GC (G, N)$ , which is the number of intermediate fields $E$ with $K \…

math.RA2019★ 23 cited

Bi-skew braces and Hopf Galois structures

Lindsay N. Childs

We define a bi-skew brace to be a set $G$ with two group operations $⋆$ and $\circ$ so that $(G, \circ, ⋆)$ is a skew brace with additive group $(G, ⋆)$ and also with a…

math.RA2018

Skew braces and the Galois correspondence for Hopf Galois structures

Lindsay N. Childs

Let $L / K$ be a Galois extension of fields with Galois group $Γ$ , and suppose $L / K$ is also an $H$ -Hopf Galois extension. Using the recently uncovered connection between Hopf Galois…

math.RA2017

Bounds on the number of ideals in finite commutative nilpotent $F_{p}$ -algebras

Lindsay N. Childs, Cornelius Greither

Let $A$ be a finite commutative nilpotent $F_{p}$ -algebra structure on $G$ , an elementary abelian group of order $p^{n}$ . If $K / k$ is a Galois extension of fields with Galois…

math.RA2016★ 3 cited

On the Galois correspondence for Hopf Galois structures

Lindsay N. Childs

We study the question of the surjectivity of the Galois correspondence from subHopf algebras to subfields given by the Fundamental Theorem of Galois Theory for abelian Hopf Galois…

math.GR2016

Abelian Hopf Galois structures from almost trivial commutative nilpotent algebras

Lindsay N. Childs

Let $L / K$ be a Galois extension of fields with Galois group $G$ , an elementary abelian $p$ -group of rank $n$ for $p$ an odd prime. It is known that nilpotent $F_{p}$ -algebra…

math.NT2013

Scaffolds and Generalized Integral Galois Module Structure

Nigel P. Byott, Lindsay N. Childs, G. Griffith Elder

Let $L / K$ be a finite, totally ramified $p$ -extension of complete local fields with residue fields of characteristic $p > 0$ , and let $A$ be a $K$ -algebra acting on $L$ . We define…

On the Galois correspondence ratio for Hopf-Galois extensions arising from nilpotent Fp​-algebras

Skew left braces and the Yang-Baxter equation

On the Galois correspondence for Hopf Galois structures arising from finite radical algebras and Zappa-Szép products

Bi-skew braces and Hopf Galois structures

Skew braces and the Galois correspondence for Hopf Galois structures

Bounds on the number of ideals in finite commutative nilpotent Fp​-algebras

On the Galois correspondence for Hopf Galois structures

Abelian Hopf Galois structures from almost trivial commutative nilpotent algebras

Scaffolds and Generalized Integral Galois Module Structure

On the Galois correspondence ratio for Hopf-Galois extensions arising from nilpotent $F_{p}$ -algebras

Bounds on the number of ideals in finite commutative nilpotent $F_{p}$ -algebras