Proper ideal

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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