field of quotients
field of quotients noun: 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: (a,b)+(a',b')=(ab'+a'b,bb'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b)≡(a',b') if and only if ab'=a'b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a).
Noun
field of quotients (plural fields of quotients)
- 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: (a,b)+(a',b')=(ab'+a'b,bb'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b)≡(a',b') if and only if ab'=a'b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a).
- Synonyms:
- field of fractions
field of quotients meaning in Tamil
field of quotients in Tamil
- ஈவு புலம்
Synonyms of field of quotients
Forms of field of quotients
| plural | fields of quotients |
|---|
Questions about field of quotients
- What does field of quotients mean?
- Field of quotients means 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: (a,b)+(a',b')=(ab'+a'b,bb'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b)≡(a',b') if and only if ab'=a'b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a).
- What is field of quotients in Tamil?
- Field of quotients in Tamil is ஈவு புலம். See Field of quotients meaning in Tamil.
- What part of speech is field of quotients?
- Field of quotients is a noun.
- What is the plural of field of quotients?
- The plural of field of quotients is fields of quotients.
Words near field of quotients in the dictionary
Source and license
Adapted from Wiktionary: field of quotients (page history and authors); field of quotients (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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