Goldie Ranks of Skew Power Series Rings of Automorphic Type

TL;DR

This paper proves that the Goldie rank of a semiprime, right noetherian ring remains unchanged when extended to a skew power series ring of automorphic type, with applications to induced ideals.

Contribution

It establishes the equality of Goldie ranks between a ring and its skew power series extension, a novel result in ring theory.

Findings

Goldie ranks of A and B are equal.

The result applies to semiprime, right noetherian rings with automorphisms.

Applications to induced ideals are discussed.

Abstract

Let A be a semprime, right noetherian ring equipped with an automorphism alpha, and let B := A[[y; alpha]] 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.