ON THE GRADED ANNIHILATORS OF RIGHT MODULES OVER THE FROBENIUS SKEW POLYNOMIAL RING

摘要

Let R be a commutative Noetherian ring of prime characteristic and M be an xdivisible right R[x, f]-module that is Noetherian as R-module. We give an affirmative answer to the question of Sharp and Yoshino in the case where R is semilocal and prove that the set of graded annihilators of R[x, f]-homomorphic images of M is finite. We also give a counterexample in the general case.