The Structure of Schur Rings over Cyclic Groups of Square-Free Order

Mikhail Muzychuk

doi:10.1023/a:1005959008545

The Structure of Schur Rings over Cyclic Groups of Square-Free Order

Mikhail Muzychuk

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We give the complete classification of Schur rings over cyclic groups of square-free order. In this classification we use the topological language originally suggested by Ya. Yu. Gol'fand. Each Schur ring over Ζ_n is uniquely determined by a finite topology L on the set of prime divisors of n and by a family {G_P}_P∈L of finite groups satisfying an additional condition.

Original language	English
Pages (from-to)	163-181
Number of pages	19
Journal	Acta Applicandae Mathematicae
Volume	52
Issue number	1-3
DOIs	https://doi.org/10.1023/a:1005959008545
State	Published - 1 Jan 1998
Externally published	Yes

Keywords

Basic set
Group algebra
Lattice
S-ring
Schur ring

ASJC Scopus subject areas

Applied Mathematics

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10.1023/a:1005959008545

Cite this

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title = "The Structure of Schur Rings over Cyclic Groups of Square-Free Order",

abstract = "We give the complete classification of Schur rings over cyclic groups of square-free order. In this classification we use the topological language originally suggested by Ya. Yu. Gol'fand. Each Schur ring over Ζn is uniquely determined by a finite topology L on the set of prime divisors of n and by a family \{GP\}P∈L of finite groups satisfying an additional condition.",

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AB - We give the complete classification of Schur rings over cyclic groups of square-free order. In this classification we use the topological language originally suggested by Ya. Yu. Gol'fand. Each Schur ring over Ζn is uniquely determined by a finite topology L on the set of prime divisors of n and by a family {GP}P∈L of finite groups satisfying an additional condition.

KW - Basic set

KW - Group algebra

KW - Lattice

KW - S-ring

KW - Schur ring

UR - https://www.scopus.com/pages/publications/1442268927

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DO - 10.1023/a:1005959008545

M3 - Article

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ER -

The Structure of Schur Rings over Cyclic Groups of Square-Free Order

Abstract

Keywords

ASJC Scopus subject areas

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