Quotient field：大學基礎代數
大學基礎代數
則M是R的一個maximalideal若且唯若R/M這個quotientring是一個field.Proof.首先觀察由假設可知R/M是一個commutativeringwith1,所以R/M是.。其他文章還包含有：「AbstractAlgebra14.4」、「AbstractAlgebraLecturesPart17」、「Fieldoffractions」、「FieldTheoryQuotientfields」、「Lecture6」、「TheQuotientFieldofanIntegralDomain」、「Whatisthedefinitionofaquotientfieldonanarbitrary...」
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Abstract Algebra 14.4
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Abstract Algebra Lectures Part 17
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Field of fractions
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Quotient field redirects here. Not to be confused with Quotient ring. In abstract algebra, the field of fractions of an integral domain is the smallest field ...
Field TheoryQuotient fields
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< Field Theory. Definition (quotient field): Let R -displaystyle R} R be an integral domain. ... is defined to be the field of formal fractions.
Lecture 6
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The field F will be called as a field of quotients (field of fractions) of an integral domain D. Theorem. Any integral domain D can be embedded in a field F.
The Quotient Field of an Integral Domain
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The standard argument for objects defined by universal properties shows that the quotient field of an integral domain is unique up to ring isomorphism.
What is the definition of a quotient field on an arbitrary ...
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A quotient object of is an equivalence class of epimorphisms from to wherever, where two such morphisms are deemed equivalent if each of them factors through ...