(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

let S be the ring of all pairs (q,s) with q,s being rational.

define (q,s) + (q',s') = (q+q',s+s')

and (q,s)(q',s') = (qs'+q's,3qq'+ss')

Prove that S is a field.

2. Relevant equations

Try proving that it is isomorphic to something else using the First homomorphism theorem for rings.

3. The attempt at a solution

I can not find a homomorphism between S and any commonly known fields like complex numbers, real numbers, rational numbers, etc

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# Finding that S is a Field

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