Indecomposable ideal

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 indecomposable or join-irreducible if it is nonzero, and cannot be expressed as a sum of two strictly smaller ideals.

Relation with other properties

Incomparable properties

• Irreducible ideal: This is the meet-irreducibility