Equicharacteristic 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

A commutative unital ring is said to be an equicharacteristic ring if the characteristic of the ring equals the characteristic of the quotient field by any maximal ideal thereof.

In particular, a local ring is an equicharacteristic local ring if the characteristic of the ring equals the characteristic of its residue field.