Kauta, John S. (2012) On a class of semihereditary crossedproduct orders. Pacific Journal of Mathematics, 259 (2). pp. 349360. ISSN 00308730
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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 crossedproduct Valgebra Af =σσεG Sxσ in a natural way, which is a Vorder in the crossedproduct Falgebra (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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