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On the codimension of modules over skew power series rings with applications to Iwasawa algebras
- Source :
-
Journal of Pure & Applied Algebra . Feb2006, Vol. 204 Issue 2, p349-367. 19p. - Publication Year :
- 2006
-
Abstract
- Abstract: The first purpose of this paper is to set up a general notion of skew power series rings S over a coefficient ring R, which are then studied by filtered ring techniques. The second goal is the investigation of the class of S-modules which are finitely generated as R-modules. In the case that S and R are Auslander regular we show in particular that the codimension of M as S-module is one higher than the codimension of M as R-module. Furthermore its class in the Grothendieck group of S-modules of codimension at most one less vanishes, which is in the spirit of the Gersten conjecture for commutative regular local rings. Finally we apply these results to Iwasawa algebras of p-adic Lie groups. [Copyright &y& Elsevier]
- Subjects :
- *ALGEBRA
*MATHEMATICAL analysis
*MATHEMATICS
*IWASAWA theory
Subjects
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 204
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 19114029
- Full Text :
- https://doi.org/10.1016/j.jpaa.2005.05.007