Abstract

For a module M R 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.

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