On a class of semihereditary crossed-product orders

Kauta, John S. (2012) On a class of semihereditary crossed-product orders. Pacific Journal of Mathematics, 259 (2). pp. 349-360. ISSN 0030-8730

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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 twococycle such that f (G × G) ⊆ S\ {0}, but we do not require that f should take values in the group of multiplicative unitsof S. One can construct a crossed-product V-algebra Af =σσεG Sxσ in a natural way, which is a Vorder in the crossed-product F-algebra (K/F, G, f ). If V is unramified and defectless in K, we show that Af is semihereditary if and only if for all σ, τ ε G and every maximal ideal M of S, f(σ,τ) ∉ M2. If in addition J(V) is not a principal ideal of V, then Af is semihereditary if and only if it is an Azumaya algebra 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 23:05
Last Modified:	01 Aug 2016 23:54
URI:	http://repository.usp.ac.fj/id/eprint/7017

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