Journal der mathematischen Ablehnungen 14 (2007) 1–5 Planar polynomials and commutative semifields two dimensional over their middle nucleus and four dimensional over their nucleus

A semifield R is a not necessarily associative ring with no zero-divisors, a multiplicative identity and left and right distributive laws. A semifield which is not a field is called proper. If a multiplicative identity is not insisted upon, then we talk of presemifields. It is an easy exercise to show any finite semifield must have prime power order, and as with finite fields we shall refer to the prime involved as the characteristic of the semifield. Th