English

Division algebras that generalize Dickson semifields

Rings and Algebras 2019-06-05 v1

Abstract

We generalize Knuth's construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension 2s22s^2 by doubling central division algebras of degree ss. Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

Keywords

Cite

@article{arxiv.1906.01329,
  title  = {Division algebras that generalize Dickson semifields},
  author = {Daniel Thompson},
  journal= {arXiv preprint arXiv:1906.01329},
  year   = {2019}
}

Comments

10 pages, work is part of author's PhD thesis

R2 v1 2026-06-23T09:40:52.194Z