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:
 * $\left({\left\{ {\text{even}, \text{odd} }\right\}, +, \times}\right)$

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