New examples of fractional dimensional semifield planes

This is a short round up of the fractional dimension of finite semifields and finite semifield planes. We show that the classical Knuth binary semifields can never be fractional dimensional and a special class of the generalized Knuth binary semifields is fractional dimensional, even though these two classes of semifields are isotopic. Finally we show that the Albert semifield An(S), where n is any odd integer, does not contain GF(23) when (n,3)=1.