Associated primes over Ore extensions

For a module MR we compute the set of associated primes of M[x;σ] over the left Ore extension R[x;σ] for any surjective endomorphism σ of R. This result leads to necessary and sufficient conditions under which the associated primes of M[x;σ] are precisely the extensions of the associated primes of M. We relate these results to previous work regarding the propagation of prime ideals of R[x;σ] and include several illustrative examples.