Proper ideal

Symbol-free definition
An ideal in a commutative unital ring is termed a proper ideal if it satisfies the following equivalent conditions:


 * The element $$1$$ of the ring, does not lie inside the ideal
 * The ideal is not equal to the whole ring

Definition with symbols
An ideal $$I$$ in a commutative unital ring $$R$$ is termed a proper ideal if it satisfies the following equivalent conditions:


 * $$1 \notin I$$
 * $$I \ne R$$