Local ring

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions

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

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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