Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 2 down vote favorite

In one of my proof for my assignment I reached a point where I have to prove that $x^9-t^9$ is irreducible in $\mathbb{Z}_7(t^9)[x]$. I am unsure weather this is irreducible. If it is, how do I prove it? Thanks in advance.

share|improve this question
1  
What is $\mathbb{Z}_7(t^9)$? Is it the field of fractions of $\mathbb{Z}_7[t^9]$ – Aleks Vlasev Oct 21 '12 at 5:09
1  
Hint: Eisenstein's Criterion. – Rankeya Oct 21 '12 at 6:00
@Rankeya: There is no prime element in $Z_7(t^9)$. – user44322 Oct 21 '12 at 21:07
@AleksVlasev Yes that is the field of fractions. – user44322 Oct 21 '12 at 21:07
Agreed, but there is a prime element in $\mathbb{Z}_7[t^9]$, which is a ring, not a field. – Rankeya Oct 21 '12 at 21:45

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.