Let R be a commutative Noetherian ring of prime characteristic and M be anx-divisible right R[x,f]-module that is Noetherian as R-module. We give anaffirmative answer to the question of Sharp and Yoshino in the case where R issemi-local and prove that the set of graded annihilators of R[x,f]-homomorphicimages of M is finite. We also give a counterexample in the general case.
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