# Proper ideal

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## Contents

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:

• $1 \notin I$
• $I \ne R$