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
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