University of Nebraska at Omaha

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19942026

most citedGiant Electroresistance in Ferroelectric Tunnel Junctions

762 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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math.NT2021★ 2 cited

On the Geometry of Numerical Ranges Over Finite Fields

Kristin A. Camenga, Brandon Collins, Gage Hoefer +4

Numerical ranges over a certain family of finite fields were classified in 2016 by a team including our fifth author. Soon afterward, in 2017 Ballico generalized these results to a…

math.NT2015

Ramified extensions of degree $p$ and their {H}opf-{G}alois module structure

G. Griffith Elder

Cyclic, ramified extensions $L / K$ of degree $p$ of local fields with residue characteristic $p$ are fairly well understood. Unless $\mbox{char}(K)=0$ and $L = K (p π_{K})$ for s…

math.NT2013★ 10 cited

Sufficient Conditions for Large Galois Scaffolds

Nigel P. Byott, G. Griffith Elder

Let $L / K$ be a finite Galois, totally ramified $p$ -extension of complete local fields with perfect residue fields of characteristic $p > 0$ . In this paper, we give conditions, valid…

math.NT2009★ 2 cited

Integral Galois Module Structure for Elementary Abelian Extensions with a Galois Scaffold

Nigel P. Byott, G. Griffith Elder

This paper justifies an assertion in (Elder, Proc AMS 137 (2009), no 4, 1193--1203) that Galois scaffolds make the questions of Galois module structure tractable. Let $k$ be a perf…

math.NT2008★ 1 cited

A valuation criterion for normal basis generators in local fields of characteristic $p$

G. Griffith Elder

Let $K$ be a complete local field of characteristic $p$ with perfect residue field. Let $L / K$ be a finite, fully ramified, Galois $p$ -extension. If $π_{L} \in L$ is a prime element, a…

math.NT2007

On the necessity of new ramification breaks

Nigel P. Byott, G. Griffith Elder

Ramification invariants are necessary, but not in general sufficient, to determine the Galois module structure of ideals in local number field extensions. This insufficiency is ass…

math.NT2006

A valuation criterion for normal bases in elementary abelian extensions

Nigel P. Byott, G. Griffith Elder

Let $p$ be a prime number and let $K$ be a finite extension of the field $Q_{p}$ of $p$ -adic numbers. Let $N$ be a fully ramified, elementary abelian extension of $K$ . Under…

On the Geometry of Numerical Ranges Over Finite Fields

Ramified extensions of degree p and their {H}opf-{G}alois module structure

Sufficient Conditions for Large Galois Scaffolds

Integral Galois Module Structure for Elementary Abelian Extensions with a Galois Scaffold

A valuation criterion for normal basis generators in local fields of characteristic p

On the necessity of new ramification breaks

A valuation criterion for normal bases in elementary abelian extensions

Ramified extensions of degree $p$ and their {H}opf-{G}alois module structure

A valuation criterion for normal basis generators in local fields of characteristic $p$