Crossed product and hereditary orders
type: Item
instance of: scholarly article
title: Crossed product and hereditary orders
zbMATH Open document ID: 0588.12013
author: Gerald Cliff
author: A. Weiss
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let L/K be a finite Galois extension of local fields and let d, e, and f be the different exponent, ramification index, and inertial degree of L/K. For a certain crossed product order \(\wedge\) over K the authors prove that a specified last order \(\wedge_ s\) in a chain is the unique minimal hereditary order in \(A=K\wedge\) containing \(\wedge\), that \(\wedge_ s\) has e/m simple modules (where m is the Schur index of A), each of dimension f over the residue class field of the ring of integers of K, and that \(s=d-(e-1)\).
Mathematics Subject Classification ID: 11S45
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 3943974
zbMATH Keywords: local fields
zbMATH Keywords: crossed product order
zbMATH Keywords: hereditary order
zbMATH Keywords: simple modules
zbMATH Keywords: Schur index
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: pjm.1986.122.333
OpenAlex ID: W2044812686
DOI: 10.2140/PJM.1986.122.333
description: scientific article; zbMATH DE number 3943974