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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Normality in group rings

Authors: V. A. Bovdi and S. Siciliano
Original publication: Algebra i Analiz, tom 19 (2007), nomer 2.
Journal: St. Petersburg Math. J. 19 (2008), 159-165
MSC (2000): Primary 16S34
Published electronically: February 1, 2008
MathSciNet review: 2333894
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ KG$ be the group ring of a group $ G$ over a commutative ring $ K$ with unity. The rings $ KG$ are described for which $ xx^\sigma=x^\sigma x$ for all $ x=\sum_{g\in G}\alpha_gg\in KG$, where $ x\mapsto x^\sigma=~\sum_{g\in G}\alpha_gf(g)\sigma(g)$ is an involution of $ KG$; here $ f: G\to U(K)$ is a homomorphism and $ \sigma$ is an antiautomorphism of order two of $ G$.

References [Enhancements On Off] (What's this?)

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Additional Information

V. A. Bovdi
Affiliation: Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
Address at time of publication: Institute of Mathematics and Informatics, College of Nyíregyháza, Sóstói út 31/b, H-4410 Nyíregyháza, Hungary

S. Siciliano
Affiliation: Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, Via Provinciale Lecce-Arnesano, 73100-LECCE, Italy

Keywords: Group ring, normality
Received by editor(s): August 31, 2006
Published electronically: February 1, 2008
Additional Notes: This research was supported by OTKA no. T 037202 and no. T 038059
Dedicated: Dedicated to Professor P.M.Gudivok on the occasion of his 70th birthday
Article copyright: © Copyright 2008 American Mathematical Society