On crossed product orders.
type: Item
instance of: scholarly article
title: On crossed product orders.
zbMATH Open document ID: 0593.16005
DOI: 10.1016/0022-314X(85)90023-X
author: H. Benz
author: H. Zassenhaus
published in: Journal of Number Theory
publication date: 1985-01-01T00:00:00Z
review text: Let \(K\) be the quotient field of a complete local Dedekind domain \(R\), and \(A\) be a central simple algebra over \(K\). The authors have considered an embedding problem of the hereditary \(R\)-order \({\mathcal O}_ Z\) of a simple subalgebra \(Z\) of \(A\) over \(K\) into the hereditary \(R\)-order \({\mathcal O}_ A\) of \(A\) [\textit{H. Benz}, J. Reine Angew. Math. 225, 30-75 (1967; Zbl 0155.09802) and \textit{H. Zassenhaus}, Number Theory and Algebra, 363-393 (1977; Zbl 0375.16007)]. In those considerations, crossed product orders played an important role. In this paper, they investigate the arithmetic of crossed products and prove the uniqueness of existence of an hereditary \(R\)-order \({\mathcal O}_ A\) of \(A\) satisfying some conditions for each crossed product order \({\mathcal O}\) and the maximal one of all crossed product orders contained in \({\mathcal O}_ A\).
reviewed by: Hideo Yokoi
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 3952984
zbMATH Keywords: central simple algebra
zbMATH Keywords: crossed product orders
MaRDI profile type: Publication
cites work: Untersuchungen zur Arithmetik in lokalen einfachen Algebren, insbesondere über maximalen Teilkörpern. I.
cites work: Q4155015
description: scientific article; zbMATH DE number 3952984