Citation
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
Abstract
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
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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 |
| Statistic Details: | View Download Statistic |
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