Twenty-Seven Element Albertian Semifields
In 1958 Abraham Adrian Albert published his findings on the now famous class of semifields known as twisted fields or, as we refer to them in this thesis, Albertian semifields. Since the publication of his findings, interest in the topic of semifields has grown and, naturally, some progress has been made in the subject, but there is still much to be studied. Moreover, the greater portion of modern efforts have been made to develop a theory of semifields, with less attention paid to more practical considerations. In this thesis, we will narrow our investigations to a specific subclass of Albert's semifields, namely, those that contain exactly twenty-seven elements. We will derive the specificequations used to compute products in the semifields of this subclass, and construct multiplication tables for both a basis of the semifield, as well as for the twenty-seven element semifield entire. Lastly, we will demonstrate that, in fact, there are only four such semifields which are unique up to an isomorphism.
Hughes, Thomas, "Twenty-Seven Element Albertian Semifields" (2016). ETD Collection for University of Texas, El Paso. AAI10250446.