USP Electronic Research Repository

Weak crossed - product orders over valuation rings

Kauta, John S. (2014) Weak crossed - product orders over valuation rings. Journal of Algebra, 402 . pp. 319-350. ISSN 0021-8693

[thumbnail of Offprint10.pdf] PDF - Published Version
Restricted to Repository staff only

Download (782kB) | Request a copy
[thumbnail of Preprint10.pdf] PDF - Accepted Version
Restricted to Registered users only

Download (219kB) | Request a copy

Abstract

Let F be a field, let V be a valuation ring of F of arbitrary Krull dimension (rank), let K be a finite Galois extension of F with group G, and let S be the integral closure of V in K. Let f:G×G↦K∖{0} be a normalized two-cocycle such that f(G×G)⊆S∖{0}, but we do not require that f should take values in the group of multiplicative units of S. One can construct a crossed-product V-order Af=∑σ∈GSxσ with multiplication given by xσsxτ=σ(s)f(σ,τ)xστ for s∈S, σ,τ∈G. We characterize semihereditary and Dubrovin crossed-product orders, under mild valuation-theoretic assumptions placed on the nature of the extension K/F.

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: 12 Mar 2014 03:25
Last Modified: 09 May 2016 23:17
URI: https://repository.usp.ac.fj/id/eprint/7230

Actions (login required)

View Item View Item