Introduction to Rings and Fields- Help

Thread starter Palindrom
Start date Dec 12, 2004
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Fields Introduction Rings

AI Thread Summary

The discussion focuses on finding an alternative method to define a homomorphism for the problem involving the isomorphism of Q[x]/(x-1) and Q[x]/(x-2). Participants suggest that both rings can be shown to be isomorphic to a third ring, specifically Q. The conversation highlights the challenge of completing homework late at night, indicating a common struggle among students. Overall, the key takeaway is the exploration of isomorphism in ring theory and the potential for simplification through a third ring comparison. The discussion emphasizes the importance of understanding ring structures in abstract algebra.

Dec 12, 2004

Palindrom

I really don't want to define a homomorphism like
psi(p(x))=p(x-1+I
I'm looking for another way to solve that next question:

Show that Q[x]/(x-1) is isomorphic to Q[x]/(x-2).
Any ideas?
Thanks in advance.

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Dec 12, 2004

Hurkyl

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You could show they're both isomorphic to a third ring...

Dec 12, 2004

Palindrom

Hurkyl said:

You could show they're both isomorphic to a third ring...

Of course, they're both isomorphic to Q... I really shouldn't do HW at 11 pm... Thanks!

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