Crossed product orders over valuation rings II: Tamely ramified crossed product algebras

Kauta, John S. and Marubayashi, H. and Miyamoto, H. (2003) Crossed product orders over valuation rings II: Tamely ramified crossed product algebras. Bulletin of the London Mathematical Society, 35 (4). pp. 541-552. ISSN 0024-6093

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Abstract

Let V be a commutative valuation domain of arbitrary K rull-dimension, with quotient field F, let K be a finite Galois extension of F with group G, and let S be the integral closure of V in K. Suppose that one has a 2-cocycle on G that takes values in the group of units of S. Then one can form the crossed product of G over S, S * G, which is a V-order in the central simple F-algebra K * G. If S * G is assumed to be a Dubrovin valuation ring of K * G, then the main result of this paper is that, given a suitable definition of tameness for central simple algebras, K * G is tamely ramified and defectless over F if and only if K is tamely ramified and defectless over F. The residue structure of S * G is also considered in the paper, as well as its behaviour upon passage to Henselization.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
Depositing User:	John Kauta
Date Deposited:	05 Nov 2013 22:45
Last Modified:	05 Nov 2013 22:45
URI:	https://repository.usp.ac.fj/id/eprint/7011

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