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:
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)