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.
Irreducibility of polynomial
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polynomials
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1What is $\mathbb{Z}_7(t^9)$? Is it the field of fractions of $\mathbb{Z}_7[t^9]$ – 2012-10-21
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1Hint: Eisenstein's Criterion. – 2012-10-21
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0@Rankeya: There is no prime element in $Z_7(t^9)$. – 2012-10-21
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0@AleksVlasev Yes that is the field of fractions. – 2012-10-21
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0Agreed, but there is a prime element in $\mathbb{Z}_7[t^9]$, which is a ring, not a field. – 2012-10-21