Let be a map defined by . Show that is a ring homomorphism, and is a field. QnR f())=f(V2) We were unable to trans...

Question

Question

Let $QnR$ be a map defined by $f())=f(V2)$ . Show that $\phi$ is a ring homomorphism, and $Im()$ is a field.

QnR
f())=f(V2)

Im()

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Answer 1

Answer #1

: Ql R defined b P(f)f) Let fe, fdx)e Q [x] (fe+= ( f18)= f+8)(E) =f(TEJ+ &«IEJ = 4(ftesj+ ¢ (dr), (f)) CE P- = (a) (P) Lfe). 中(fa) = 0} Long ={fe) e a x7: kenp 2 Now balroowjal fnae 22-2 is ecluci ble OVeN fietd Hence fr(ps a fieldd

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Answer 2

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