field of quotients

Noun

 * 1)  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: $$(a,b) + (a',b') = (a b' + a' b,b b')$$, 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: $$(a,b) \equiv (a', b')$$ if and only if $$a b' = a' b$$, and multiplicative inverse of a non-zero–equivalent element $$(a,b)$$ is $$(b,a)$$.