(x^2-3)

Asked Sep 14 '17 at 01:25

Active Sep 14 '17 at 02:49

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Show that $$Q[x]/(x^2-2)$$ is not isomorphic to $$Q[x]/(x^2-3)$$

I was practicing some exercises in Hungerford's abstract algebra book, I could make them all but this one. I think I have to verify if it is irreducible and thus be able to say if it is isomorphic, but I do not know how. I hope you can help me understand.

edited Sep 14 '17 at 02:49

Robert Lewis

71,180

asked Sep 14 '17 at 01:25

Hector Javier Torres

Isomorphic as a ring or as a $\mathbb{Q}$-algebra? – Leon Lang Sep 14 '17 at 01:27
3

You do understand that the first ring has a square root of $2$, and the second has a square root of $3$, right? Can you show that the first doesn’t have a square root of $3$? – Lubin Sep 14 '17 at 01:37
I believe that Q (rationals) – Hector Javier Torres Sep 14 '17 at 01:38
I added the "field-theory" and the "extension-field" tags to your post. – Robert Lewis Sep 14 '17 at 02:50

Show that Q[x] /(x^2-2) is not isomorphic to Q[x] /(x^2-3)

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