Definition
A planar ternary ring is a structure where is a nonempty set, containing distinct elements called 0 and 1, and satisfies these five axioms:
- ;
- ;
- , there is a unique such that : ;
- , there is a unique, such that ; and
- , the equations have a unique solution .
When is finite, the third and fifth axioms are equivalent in the presence of the fourth. No other pair (0', 1') in can be found such that still satisfies the first two axioms.
Read more about this topic: Planar Ternary Ring
Famous quotes containing the word definition:
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)