Counting skew monomials in the Frobenius skew polynomial ring

Abstract

We study the Frobenius skew polynomial ring over a polynomial ring in finitely many variables and show that growth function associated to the variables and the Frobenius satisfies a linear recurrence. We introduce the concept of Gelfand-Kirillov base for a finitely generated standard graded algebra over the prime field of characteristic p, where p is prime, and show its existence for the polynomial ring.

Keywords:

• Frobenius skew polynomial ring
• Gelfand-Kirillov dimension
• GK base

2020 Mathematics Subject Classification:

• 13A35
• 16S36
• 16P90

Acknowledgments

This material was prepared for the PhD dissertation at Georgia State University of the first author under the guidance of the second author. The authors benefited from the reviewer’s comments on the content of the paper which led us to make some corrections and improve our presentation as well. We thank the reviewer for their feedback.