单词 quotient ring 释义 BETA

Examples ofquotient ring

Dictionary> Examples ofquotient ringquotient ringisn’t in the Cambridge Dictionary yet. You can help!Add a definitionThis, in turn, is important for the definition of the totalquotientring.FromWikipediaThis example is from Wikipedia and may be reused under a CC BY-SA license.Then thequotientringis a field of size.FromWikipediaThis 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.FromWikipediaThis example is from Wikipedia and may be reused under a CC BY-SA license.Then thequotientringis isomorphic to the ring of tessarines.FromWikipediaThis 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.FromWikipediaThis example is from Wikipedia and may be reused under a CC BY-SA license.It should not be confused with aquotientring.FromWikipediaThis 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.FromWikipediaThis 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.FromWikipediaThis 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.FromWikipediaThis 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.FromWikipediaThis 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.FromWikipediaThis example is from Wikipedia and may be reused under a CC BY-SA license.

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