Structure of normal twisted group rings

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2 Citations (Scopus)

Abstract

Let KλG be the twisted group ring of a group G over a commutative ring K with 1, and let λ be a factor set (2-cocycle) of G over K. Suppose f : G → U(K) is a map from G onto the group of units U(K) of the ring K satisfying f(1) = 1. If cursive Greek chi = Σg∈G αgug ∈ KλG then we denote Σg∈G αgf(g)u-1g by cursive Greek chif and assume that the map cursive Greek chi → cursive Greek chif is an involution of KλG. In this paper we describe those groups G and commutative rings K for which KλG is f-normal, i.e. cursive Greek chicursive Greek chif = cursive Greek chif cursive Greek chi for all cursive Greek chi ∈ KλG.

Original languageEnglish
Pages (from-to)279-293
Number of pages15
JournalPublicationes Mathematicae
Volume51
Issue number3
Publication statusPublished - 1997
Externally publishedYes

Keywords

  • Crossed products
  • Group rings
  • Ring property
  • Twisted group rings

ASJC Scopus subject areas

  • Mathematics(all)

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