For example, what is the difference between

and ?

What do they look like?

Is ?

I'm having trouble "getting it" if that makes sense. :confused:

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- March 17th 2009, 08:35 PMelectricjaguarI don't really understand polynomial quotient rings
For example, what is the difference between

and ?

What do they look like?

Is ?

I'm having trouble "getting it" if that makes sense. :confused: - March 17th 2009, 08:52 PMGaloisTheory1
- March 17th 2009, 11:08 PMelectricjaguar
Thank you, I have more questions that I'm just going to put in this thread so as not to cloud up the forum.

Is it true that contains a unique maximal ideal, but does not? I think this is the case by the correspondence theorem

Also, I can see why , but why is ? - March 18th 2009, 05:01 AMelectricjaguar
I also have a question about . Isn't one of its elements which has a root in , namely, x = 0? Doesn't this show that this element is reducible and hence the quotient is not a field?

edit: nevermind - March 18th 2009, 09:47 AMGaloisTheory1