Local ring

This article defines a property of commutative rings

Definition for commutative rings

Symbol-free definition

A commutative unital ring is termed a local ring if it has a unique maximal ideal.

Definition with symbols

Fill this in later

Definition for noncommutative rings

Further information: Local ring (noncommutative rings)

Relation with other properties

Stronger properties

• Field
• Regular local ring

Weaker properties

• Semilocal ring
• Quasilocal ring

Conjunction with other properties

• Local Noetherian ring
• Local Artinian ring
• Local domain