In the case of the definition used by Chatters and the reviewer, this generalizes a result of K. A. Brown [ibid. 32, 426-438 (1985; Zbl 0589.16013)]. The paper contains several examples but one of these, Example 1 of Section 3, appears to the reviewer to be incorrect as stated....
J Lond Math Soc (2) 30:465-467Chatters AW, Hajarnavis CR (1980) Rings with chain conditions. Research notes in mathematics, vol 44. Pitman, LondonChevalley C (1951) Deux theoremes d'arithmetique. J Math Soc Jpn 3:36-44Cohn PM (1974) Algebra. Wiley, Chichester. 2nd edition, 1989...
ChattersA.W.Taylor & Francis GroupCommunications in AlgebraA. W. Chatters and J. Clark, Group rings which are unique factorisation rings, Comm. in Algebra , 19 (1991), 585–598.A. W. Chatters and J. Clark, 'Group rings which are unique factorisation rings', Comm. Algebra 19 (1991)...
We show that the quantum coordinate ring of a semisimple group is a unique factorisation domain in the sense of Chatters and Jordan in the case where the deformation parameter q is a transcendental element.doi:10.1112/blms/bdm025Launois S...
This general result applies to many quantum algebras; in particular, generic quantum matrices and quantized enveloping algebras of the nilpotent part of a semisimple Lie algebra are unique factorisation domains in the sense of Chatters. The result also extends to generic quantum grassmannians (by ...