# Planar Ternary Ring

In mathematics, a ternary ring is an algebraic structure consisting of a non-empty set and a ternary mapping, and a planar ternary ring (PTR) or ternary field is special sort of a ternary ring used by Hall (1943) to give coordinates to projective planes. A planar ternary ring is not a ring in the traditional sense.

### Other articles related to "ternary, ring, planar ternary ring, planar ternary rings":

Pólya Enumeration Theorem - Examples - Rooted Ternary Trees
... The set T3 of rooted ternary trees consists of rooted trees where every node has exactly three children (leaves or subtrees) ... Small ternary trees are shown at right ... Note that ternary trees with n vertices are equivalent to trees with n vertices of degree at most 3 ...
Ternary Tree
... In computer science, a ternary tree is a tree data structure in which each node has at most three child nodes, usually distinguished as "left", “mid ... Ternary trees are used to implement Ternary search trees and Ternary heaps ...
Projective Plane - Affine Planes - Generalized Coordinates
... One can construct a coordinate "ring"—a so-called planar ternary ring (not a genuine ring)—corresponding to any projective plane ... A planar ternary ring need not be a field or division ring, and there are many projective planes that are not constructed from a division ring ... because the octonions do not form a division ring ...
Planar Ternary Ring - Connection With Projective Planes
... Given a planar ternary ring, one can construct a projective plane in this way ( is an extra symbol not in ) We define the incidence relation in this way One can prove that every ... However, two nonisomorphic planar ternary rings can lead to the construction of isomorphic projective planes ...

### Famous quotes containing the word ring:

Full fathom five thy father lies,
Of his bones are coral made;
Those are pearls that were his eyes;
Nothing of him that doth fade,
But doth suffer a sea-change
Into something rich and strange.
Sea-nymphs hourly ring his knell:
Ding-dong.
Hark! Now I hear them—ding-dong bell.
William Shakespeare (1564–1616)