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单词 quotient ring
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Examples ofquotient ring

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This, in turn, is important for the definition of the totalquotientring.
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Then thequotientringis a field of size.
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In this context, thequotientringconcept is one of the most powerful unifiers.
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Then thequotientringis isomorphic to the ring of tessarines.
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Unfortunately, in general, the totalquotientringdoes not produce a presheaf much less a sheaf.
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It should not be confused with aquotientring.
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The naive solution is to replace the fraction field by the totalquotientring, that is, to invert every element that is not a zero divisor.
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Any nonzero element of thequotientringwill differ by a null sequence from such a sequence, and by taking pointwise inversion we can find a representative inverse element.
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It is the same construction used for quotient groups and quotient rings.
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Indeed, this universal property can be used to "define" quotient rings and their natural quotient maps.
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Maximal ideals are important because the quotient rings of maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields.
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These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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更新时间：2025/10/25 12:32:42