In mathematics, an algebraic structure consisting of a non-empty set and a ternary mapping may be called a ternary system. A planar ternary ring (PTR) or ternary field is a special type of ternary system used by Marshall Hall to construct projective planes by means of coordinates. A planar ternary ring is not a ring in the traditional sense, but any field gives a planar ternary ring where the operation is defined by . Thus, we can think of a planar ternary ring as a generalization of a field where the ternary operation takes the place of both addition and multiplication.