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)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)