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 A n ( S ) , where n is any odd integer, does not contain G F ( 2 3 ) when ( n , 3 ) = 1 .