Equicharacteristic ring: Difference between revisions
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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. | 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. | In particular, a [[local ring]] is an [[equicharacteristic local ring]] if the characteristic of the ring equals the characteristic of its residue field. | ||
Latest revision as of 16:19, 12 May 2008
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.