V. A. Bovdi, S. Siciliano, “Normality in group rings”, Algebra i Analiz, 19:2 (2007), 1–9; St. Petersburg Math. J., 19:1 (2008), 159

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Algebra i Analiz, 2007, Volume 19, Issue 2, Pages 1–9 (Mi aa110)

This article is cited in 4 scientific papers (total in 4 papers)

Research Papers

Normality in group rings

V. A. Bovdi^ab, S. Siciliano^c

^a Institute of Mathematics, University of Debrecen, Debrecen, Hungary
^b Institute of Mathematics and Informatics, College of Nyíregyháza, Nyíregyháza, Hungary
^c Dipartimento di Matematica "E. De Giorgi", Università degli Studi di Lecce, Lecce, Italy

Full-text PDF (137 kB) Citations (4)

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Abstract: Let

K G

$KG$ be the group ring of a group

G

$G$ over a commutative ring

K

$K$ with unity. The rings

K G

$KG$ are described for which

x x^{σ} = x^{σ} x

$xx^\sigma=x^\sigma x$ for all

x = \sum_{g \in G} α_{g} g \in K G

$x=\sum_{g\in G}\alpha_gg\in KG$ , where

x \mapsto x^{σ} = \sum_{g \in G} α_{g} f (g) σ (g)

$x\mapsto x^\sigma=\sum_{g\in G}\alpha_gf(g)\sigma(g)$ is an involution of

K G

$KG$ ; here

f : G \to U (K)

$f\colon G\to U(K)$ is a homomorphism and

σ

$\sigma$ is an antiautomorphism of order two of

G

$G$ .

Keywords: Group ring, normality.

Received: 31.08.2006

English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 1, Pages 159–165
DOI: https://doi.org/10.1090/S1061-0022-08-00991-6

Bibliographic databases:

Document Type: Article

MSC: 16S34

Language: English

Citation: V. A. Bovdi, S. Siciliano, “Normality in group rings”, Algebra i Analiz, 19:2 (2007), 1–9; St. Petersburg Math. J., 19:1 (2008), 159–165

Citation in format AMSBIB

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\paper Normality in group rings

\jour Algebra i Analiz

\yr 2007

\vol 19

\issue 2

\pages 1--9

\mathnet{http://mi.mathnet.ru/aa110}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2333894}

\zmath{https://zbmath.org/?q=an:1200.16036}

\elib{https://elibrary.ru/item.asp?id=9487745}

\transl

\jour St. Petersburg Math. J.

\yr 2008

\vol 19

\issue 1

\pages 159--165

\crossref{https://doi.org/10.1090/S1061-0022-08-00991-6}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267653200001}

Linking options:

https://www.mathnet.ru/eng/aa110

https://www.mathnet.ru/eng/aa/v19/i2/p1

This publication is cited in the following 4 articles:

Holguin-Villa A., Castillo J.H., “Normal Group Algebras”, Commun. Algebr., 48:10 (2020), 4391–4402
Grishkov A.N., Rasskazova M., Siciliano S., “Normal enveloping algebras”, Pacific J. Math., 257:1 (2012), 131–141
Joe Gildea, Faye Monaghan, “Units of some group algebras of groups of order $12$ over any finite field of characteristic $3$ ”, Algebra Discrete Math., 11:1 (2011), 46–58
Gildea J., “The centre of the maximal $p$ -subgroup of $\mathcal U(\mathbb F_{p^k}D_{2p})$ ”, Glasg. Math. J., 51:3 (2009), 651–657

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	92
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