Finite Semifields: a Brief History and Current Directions

摘要

A finite semifield is a finite division ring with an unit element Finite semifields in which the multiplication is not associative were discovered by L. E. Dickson in 1905; the connection with finite projective geometry was not immediately recognized. Following a brief discussion of the history, we will examine the many directions the current research has taken following Knuth's 1965 paper.