Template:Prime-quotient-closed idp: Difference between revisions
(New page: ===Closure under quotients by prime ideals=== {{quotation|''This property of integral domains is prime-quotient-closed: the quot...) |
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===Closure under quotients by prime ideals=== | ===Closure under quotients by prime ideals=== | ||
{{quotation|''This [[property of integral domains]] is [[prime-quotient-closed property of integral domains|prime-quotient-closed]]: the quotient of any integral domain satisfying this property by a [[prime ideal]] also satisfies the property. Note that we need the ideal to be prime for the quotient to also be an integral domain.''<br>[[:Category:Prime-quotient-closed properties of integral domains|View other prime-quotient-closed properties of integral domains]]}} | {{quotation|''This [[property of integral domains]] is [[prime-quotient-closed property of integral domains|prime-quotient-closed]]: the [[quotient ring|quotient]] of any [[integral domain]] satisfying this property by a [[prime ideal]] also satisfies the property. Note that we need the ideal to be prime for the quotient to also be an integral domain.''<br>[[:Category:Prime-quotient-closed properties of integral domains|View other prime-quotient-closed properties of integral domains]]}} | ||
Revision as of 00:37, 6 February 2009
Closure under quotients by prime ideals
This property of integral domains is prime-quotient-closed: the quotient of any integral domain satisfying this property by a prime ideal also satisfies the property. Note that we need the ideal to be prime for the quotient to also be an integral domain.
View other prime-quotient-closed properties of integral domains