field of quotients

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Noun

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field of quotients (plural fields of quotients)

  1. (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:  , the multiplicative operator is defined coordinate-wise, the zero is  , the unity is  , the additive inverse of   is  , equivalence is defined like so:   if and only if  , and multiplicative inverse of a non-zero–equivalent element   is  .

Synonyms

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