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How to pronounce “field of quotients”
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Pronunciation guide for field of quotients
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- Practice the English pronunciation of field of quotients with real speech in context.
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- Definition summary
- (algebra) A field all of whose elements can be represented as ordered pairs each of whose components belong to a given integral domain, such that the second component is non-zero, and so that the additive operator is defined like so:
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A Deep Dive Into “field of quotients”
Meaning
- [Noun]
- (algebra) A field all of whose elements can be represented as ordered pairs each of whose components belong to a given integral domain, such that the second component is non-zero, and so that the additive operator is defined like so:
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- =
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- {\displaystyle (a,b)+(a',b')=(ab'+a'b,bb')}
- , the multiplicative operator is defined coordinate-wise, the zero is
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- {\displaystyle (0,1)}
- , the unity is
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- 1
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- {\displaystyle (1,1)}
- , the additive inverse of
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- {\displaystyle (a,b)}
- is
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- {\displaystyle (-a,b)}
- , equivalence is defined like so:
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- ≡
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- {\displaystyle (a,b)\equiv (a',b')}
- if and only if
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- {\displaystyle ab'=a'b}
- , and multiplicative inverse of a non-zero–equivalent element
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- {\displaystyle (a,b)}
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- {\displaystyle (b,a)}
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Practice Nearby Words
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Similar Sounds
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