Finite 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

Any integral domain satisfying this property of commutative unital rings, must be a field

Definition

A commutative unital ring is termed finite if its underlying set has finite cardinality.

Relation with other properties

Weaker properties

• Artinian ring
• Zero-dimensional ring
• Noetherian ring

Metaproperties

Closure under taking subrings

Any subring of a commutative unital ring with this property, also has this property
View other subring-closed properties of commutative unital rings

Closure under taking quotient rings

This property of commutative unital rings is quotient-closed: the quotient ring of any ring with this property, by any ideal in it, also has this property

View other quotient-closed properties of commutative unital rings