Abstract Dickson’s commutative semifields are an important class of finite division algebras. We generalize Dickson’s construction over any base field by doubling not just finite field extensions (which would correspond to the classical setup), but also central simple algebras. The latter case yields division algebras which are no longer commutative nor associative. We compute their automorphisms.

中文翻译：

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Dickson 交换除法代数的推广

摘要 Dickson 交换半域是一类重要的有限除法代数。我们通过不仅将有限域扩展（这将对应于经典设置）加倍，而且将中心简单代数加倍，将 Dickson 的构造推广到任何基域上。后一种情况产生不再可交换或结合的除法代数。我们计算它们的自同构。