A neofield of order v, Nv( + , •), is an algebraic system of v elements including 0 and 1,0 ≠ 1, with two binary operations + and • such that (Nv, + ) is a loop with identity element 0; (Nv*, •) is a group with identity element 1 (where Nv* = Nv\﹛0﹜) and every element of Nv
is both right and left distributive (i.e., (y + z)x = yx + zx and x(y + z) = xy + xz for all
y, z
∈ Nv).