Goldie Ranks of Skew Power Series Rings of Automorphic Type

2008/12/10 by Edward S. Letzter, Linhong Wang, Letzter, Edward S. +1
Mathematics · #16P40 #16W60 #16W70 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16P40 #msc:16W60 #msc:16W70

paper · pdf · doi:10.48550/arxiv.0812.2010

Revised. To appear in Communications in Algebra

arxiv created 2011/01/14 · arxiv updated 2011/01/17

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.

Related

• S-Noetherian generalized power series rings
• Goldie twisted partial skew power series rings
• The ascending chain condition for principal left or right ideals of skew generalized power series rings
• Skew power series rings over a prime base ring
• Skew power series rings with automorphisms of finite inner order