On the Graded Annihilators of Right Modules Over the Frobenius Skew Polynomial Ring

Abstract

Let R be a commutative Noetherian ring of prime characteristic and M be an x-divisible 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.

Key Words:

• Commutative Noetherian ring
• Prime characteristic
• Skew polynomial ring

2010 Mathematics Subject Classification:

• 13A35
• 13E05
• 16S36

ACKNOWLEDGMENTS

I would like to thank and express my deepest gratitude to my MSc supervisor, Professor Hossein Zakeri, for his valuable comments, patience, and encouragement during preparation of this article and my thesis.

Notes

Communicated by S. Bazzoni.

Dedicated to Professor Hossein Zakeri.