On commutativity of completely prime gamma-rings
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 commutati...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30157/ http://psasir.upm.edu.my/id/eprint/30157/1/30157.pdf |
| _version_ | 1848846598543507456 |
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| author | Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra |
| author_facet | Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra |
| author_sort | Rakhimov, Isamiddin Sattarovich |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T09:05:15Z |
| format | Article |
| id | upm-30157 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:15Z |
| publishDate | 2013 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301572015-05-27T02:18:35Z http://psasir.upm.edu.my/id/eprint/30157/ On commutativity of completely prime gamma-rings Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra 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. Universiti Putra Malaysia Press 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30157/1/30157.pdf 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 http://einspem.upm.edu.my/journal/volume7.2.php |
| spellingShingle | Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra On commutativity of completely prime gamma-rings |
| title | On commutativity of completely prime gamma-rings |
| title_full | On commutativity of completely prime gamma-rings |
| title_fullStr | On commutativity of completely prime gamma-rings |
| title_full_unstemmed | On commutativity of completely prime gamma-rings |
| title_short | On commutativity of completely prime gamma-rings |
| title_sort | on commutativity of completely prime gamma-rings |
| url | http://psasir.upm.edu.my/id/eprint/30157/ http://psasir.upm.edu.my/id/eprint/30157/ http://psasir.upm.edu.my/id/eprint/30157/1/30157.pdf |