Show that this ring is semi-simple
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Let $mathbb{F}_q$ be a field of order $q = p^m$ , where $p$ is the characteristic of the field; a prime. Consider the ring $$R_n = mathbb{F}_q[x]/langle x^n - 1 rangle $$ Now, I've read that this ring is semi-simple when $p$ does not divide $n$ , but no proof was given. Does anyone know how to prove it or somewhere where I can read the proof? Thank you.
abstract-algebra reference-request ring-theory semi-simple-rings
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asked Dec 3 '18 at 13:58
the man the man
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