On the structure of basic sets of Schur rings over cyclic groups
type: Item
instance of: scholarly article
title: On the structure of basic sets of Schur rings over cyclic groups
zbMATH Open document ID: 0810.20005
author: Mikhail Muzychuk
published in: Journal of Algebra
publication date: 1994-11-06T00:00:00Z
review text: The author proves the following conjecture of M. Klin: Two Schur rings defined over the same cyclic group are isomorphic iff they coincide. (Here the definition of isomorphism involves the preservation of the Hadamard product \((\sum x_ g g) \circ (\sum y_ g g) = \sum(x_ g y_ g)g\) and the involution \(\sum x_ g g \mapsto \sum x_ g g^{-1}\) as well.) The main tool in the sophisticated proof is a useful description of basic sets with a trivial radical.
reviewed by: Péter P. Pálfy
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 682589
zbMATH Keywords: isomorphism of Schur rings
zbMATH Keywords: cyclic groups
zbMATH Keywords: Hadamard product
zbMATH Keywords: basic sets
MaRDI profile type: Publication
full work available at URL: jabr.1994.1302
OpenAlex ID: W2030480099
DOI: 10.1006/JABR.1994.1302
description: scientific article; zbMATH DE number 682589