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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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This example is from Wikipedia and may be reused under a CC BY-SA license.Then thequotientringis a field of size.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In this context, thequotientringconcept is one of the most powerful unifiers.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Then thequotientringis isomorphic to the ring of tessarines.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Unfortunately, in general, the totalquotientringdoes not produce a presheaf much less a sheaf.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It should not be confused with aquotientring.
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This example is from Wikipedia and may be reused under a CC BY-SA license.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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This example is from Wikipedia and may be reused under a CC BY-SA license.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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This example is from Wikipedia and may be reused under a CC BY-SA license.It is the same construction used for quotient groups and quotient rings.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Indeed, this universal property can be used to "define" quotient rings and their natural quotient maps.
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This example is from Wikipedia and may be reused under a CC BY-SA license.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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This example is from Wikipedia and may be reused under a CC BY-SA license.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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