Definition:Parity Ring

Definition
The parity ring is the ring of two elements which defines the nature of the parity of integers under addition and multiplication:
 * $\struct {\set {\text{even}, \text{odd} }, +, \times}$

Cayley Tables
The parity ring can be described completely by showing its Cayley tables:

Also see

 * Parity Ring is Ring
 * Parity Ring is Smallest Field
 * Isomorphism between Ring of Integers Modulo 2 and Parity Ring