# Proper ideal

From Commalg

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 of the ring, does
*not*lie inside the ideal - The ideal is not equal to the whole ring

### Definition with symbols

An ideal in a commutative unital ring is termed a **proper ideal** if it satisfies the following equivalent conditions: