Hi guys, I was wondering how I can prove that in the field is irreducible? I know how to do it if the degree is 3 or less, but here I have no idea.. Thanks in advance, Orbis
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Originally Posted by Orbis Hi guys, I was wondering how I can prove that in the field is irreducible? I know how to do it if the degree is 3 or less, but here I have no idea.. Thanks in advance, Orbis It's easy to see there are no linear factors. As for quadratic terms, WLOG its ok to assume the two constant terms are and , since and . So we have The term tells us that . But the term tells us that . This is impossible, hence is irreducible in .
Last edited by chiph588@; April 4th 2010 at 07:49 PM.
Ah, so simple! I was thinking along the lines of proving that was a maximal ideal, but that wasn't getting me anywhere. Thanks for the quick reply! Orbis
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