Proper ideal

This article is about a basic definition in commutative algebra. View a complete list of basic definitions in commutative algebra

This article defines a property of an ideal in a commutative unital ring |View other properties of ideals in commutative unital rings

Definition

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:

• $1 \notin I$
• $I \ne R$