Conversely, given a planar ternary ring (R, T), a projective plane can be constructed (see below). The relationship is not one to one. A projective plane may be associated with several non-isomorphic planar ternary rings. The ternary operator T can be used to produce two binary operators on the set R, by: a + b = T(a, 1, b), and a ⋅ b = T(a, b, 0). The ternary operator is linear if . When the set of coordinates of a projective plane actually form a ring, a linear ternary operator may be defined in this way, using the ring operations on the right, to produce a planar ternary ring.
Conversely given a planar ternary ring (R T) a projective plane can be constructed (see below) The relationship is not one to one A projective plane may be associated with several non-isomorphic planar ternary rings The ternary operator T can be used to produce two binary operators on the set R by a + b = T(a 1 b) and a ⋅ b = T(a b 0) The ternary operator is linear if  When the set of coordinates of a projective plane actually form a ring a linear ternary operator may be defined in this way using the ring operations on the right to produce a planar ternary ring