Permanent link to this recordhttp://hdl.handle.net/20.500.12613/6052
MetadataShow full item record
AbstractWe study the "q-commutative" power series ring R:= k q[[x 1,···,x n]], defined by the relations x ixj = q ijx jx i, for mulitiplicatively antisymmetric scalars q ij in a field k. Our results provide a detailed account of prime ideal structure for a class of noncommutative, complete, local, noetherian domains having arbitrarily high (but finite) Krull, global, and classical Krull dimension. In particular, we prove that the prime spectrum of R is normally separated and is finitely stratified by commutative noetherian spectra. Combining this normal separation with results of Chan, Wu, Yekutieli, and Zhang, we are able to conclude that R is catenary. Following the approach of Brown and Goodearl, we also show that links between prime ideals are provided by canonical automorphisms. Moreover, for sufficiently generic q ij, we find that R has only finitely many prime ideals and is a UFD (in the sense of Chatters). © Springer Science+Business Media B.V. 2010.
Citation to related workSpringer Science and Business Media LLC
Has partAlgebras and Representation Theory
ADA complianceFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact email@example.com