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- Title
Prime Ideals of q-Commutative Power Series Rings.
- Authors
Letzter, Edward; Wang, Linhong
- Abstract
We study the ' q-commutative' power series ring R: = k[[ x,..., x]], defined by the relations x x = q x x, for mulitiplicatively antisymmetric scalars q 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, we find that R has only finitely many prime ideals and is a UFD (in the sense of Chatters).
- Subjects
POWER series; COMMUTATIVE algebra; NOETHERIAN rings; AUTOMORPHISMS; NONCOMMUTATIVE algebras
- Publication
Algebras & Representation Theory, 2011, Vol 14, Issue 6, p1003
- ISSN
1386-923X
- Publication type
Article
- DOI
10.1007/s10468-010-9225-7