Abstract
We continue the first and second authors’ study of q-commutative power series rings and Laurent series rings
, specializing to the case in which the commutation parameters qij are all roots of unity. In this setting, R is a PI algebra, and we can apply results of De Concini, Kac, and Procesi to show that L is an Azumaya algebra whose degree can be inferred from the qij. Our main results establish an exact criterion (dependent on the qij) for determining when the centers of L and R are commutative Laurent series and commutative power series rings, respectively. In the event this criterion is satisfied, it follows that L is a unique factorization ring in the sense of Chatters and Jordan, and it further follows, by results of Dumas, Launois, Lenagan, and Rigal, that R is a unique factorization ring.
2010 Mathematics Subject Classification:
Acknowledgement
We are grateful to the referee for the insightful comments and useful suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.