Goldie Ranks of Skew Power Series Rings of Automorphic Type

Abstract

Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B: = A[[y; α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals.

Key Words:

• Goldie Rank
• Noncommutative noetherian ring
• Prime ideal
• Skew Laurent series
• Skew power series

2010 Mathematics Subject Classification:

• Primary 16W60
• Secondary 16W70, 16P40

ACKNOWLEDGMENTS

Most of the material in this note originally formed a part (since excised) of our article [7]. We thank the original referee of [7] for remarks that helped us clarify the exposition. We also thank the referees of this article for pointing out significant simplifications in our approach, most notably in (2.6) and (2.7).

Research of the first author supported in part by grants from the National Security Agency.

Notes

Communicated by E. Kirkwan.