-pseudoreguli of and scattered semifields of order

Abstract: In this paper, we study rank two semifields of order that are of scattered type. The known examples of such semifields are some Knuth semifields, some Generalized Twisted Fields and the semifields recently constructed in Marino et al. (in press) for . Here, we construct new infinite families of rank two scattered semifields for any q odd prime power, with ; for any , such that and for any with . Both the construction and the proof that these semifields are new, rely on the structure of the linear set and the so-called pseudoregulus associated to these semifields. [Copyright &y& Elsevier]