Template:Localization-closed curing property: Difference between revisions

Latest revision as of 00:28, 6 February 2009

Closure under taking localizations

This property of commutative unital rings is closed under taking localizations: the localization at a multiplicatively closed subset of a commutative unital ring with this property, also has this property. In particular, the localization at a prime ideal, and the localization at a maximal ideal, have the property.
View other localization-closed properties of commutative unital rings

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	===Closure under taking localizations===		===Closure under taking localizations===
	{{quotation\|''This [[property of commutative unital rings]] is [[localization-closed property of commutative unital rings\|closed under taking localizations]]: the [[localization at a ~~prime ideal~~]] of a [[commutative unital ring]] with this property, also has this property''<br>[[:Category:Localization-closed properties of commutative unital rings\|View other localization-closed properties of commutative unital rings]]}}<includeonly>[[Category:Localization-closed properties of commutative unital rings]]</includeonly>		{{quotation\|''This [[property of commutative unital rings]] is [[localization-closed property of commutative unital rings\|closed under taking localizations]]: the [[localization at a multiplicatively closed subset]] of a [[commutative unital ring]] with this property, also has this property. In particular, the [[localization at a prime ideal]], and the [[localization at a maximal ideal]], have the property.''<br>[[:Category:Localization-closed properties of commutative unital rings\|View other localization-closed properties of commutative unital rings]]}}<includeonly>[[Category:Localization-closed properties of commutative unital rings]]</includeonly>