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On commutativity of completely prime gamma-rings


Rakhimov, Isamiddin Sattarovich and Dey, Kalyan Kumar and Paul, Akhil Chandra (2013) On commutativity of completely prime gamma-rings. Malaysian Journal of Mathematical Sciences, 7 (2). pp. 283-295. ISSN 1823-8343


In this paper we prove that any completely prime Γ -ring M satisfying the condition aαbβc=aβbαc = ( a,b,c ∈ M and α, β∈Γ )with nonzero derivation, is a commutative integral Γ -domain if its characteristic is not two. We also show that if the characteristic of M is 2 the Γ -ring M is either commutative or is an order in a simple 4-dimensional algebra over its center. We give necessary condition in terms of derivations for belongings of an element of the Γ -ring M to the center of M when the characteristic of M is not two. If char M = 2, and a Z M ∉ ( ), then we show that the derivation is the inner derivation.

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Official URL or Download Paper: http://einspem.upm.edu.my/journal/volume7.2.php

Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Universiti Putra Malaysia Press
Keywords: Γ -ring; Completely prime Γ -ring; Centroid of Γ -rings; Annihilator; Extended centroid of Γ -rings
Depositing User: Umikalthom Abdullah
Date Deposited: 03 Jul 2014 01:57
Last Modified: 27 May 2015 02:18
URI: http://psasir.upm.edu.my/id/eprint/30157
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