Crossed product orders over valuation rings

Kauta, John S. (2001) Crossed product orders over valuation rings. Bulletin of the London Mathematical Society, 33 (5). pp. 520-526. ISSN 0024-6093

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Abstract

Let V be a commutative valuation domain of arbitrary Krull-dimension (rank), with quotient field F, and let K be a finite Galois extension of F with group G, and S the integral closure of V in K. If, in the crossed product algebra K * G, the 2-cocycle takes values in the group of units of S, then one can form, in a natural way, a 'crossed product order' S * G ⊆ K * G. In the light of recent results by H. Marubayashi and Z. Yi on the homological dimension of crossed products, this paper discusses necessary and/or sufficient valuation-theoretic conditions, on the extension K/F, for the V-order S * G to be semihereditary, maximal or Azumaya over V.

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 22:43
Last Modified:	05 Nov 2013 22:43
URI:	https://repository.usp.ac.fj/id/eprint/7008

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