Polynomial over integers ring inversion

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I do have a finite polynomial ring over finite integer ring. Defined as $Z_{q}[x]/(x^N-1)$ where $q$ is prime power. How do I find inversion of polynomial in this ring (if there exists)? I know how to find an inversion when polynomials are over $Z_p$ where $p$ is prime or other field but how about polynomial ring over ring?