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On commutativity of prime rings with generalized derivations
Other Title(s)
حول إبدالية الحلقات الأولية ذات الاشتقاقات المعممة
Joint Authors
Bashammakh, Sabah Ahmad
Dayf, Muhammad Naji
Source
Journal of King Abdulaziz University : Sciences
Issue
Vol. 26, Issue 1 (30 Jun. 2014), pp.55-65, 11 p.
Publisher
King Abdulaziz University Scientific Publishing Center
Publication Date
2014-06-30
Country of Publication
Saudi Arabia
No. of Pages
11
Main Subjects
Topics
Abstract AR
يعتبر مفهوم الاشتقاقيات المعممة تمديد لمفهوم الاشتقاقيات كراسم جمعي →F : R يحقق أن F(xy) = F(x)y + xd(y), ∀x, y ∈ R حيث d اشتقاقية غير صفرية على R هذا الراسم F يسمى اشتقاقية معممة.
و في هذا البحث أثبتنا أنه إذا كانت R حلقة أولية، U مثالي لي بحيث أن u2 ∈ U لكل u ∈ U و F اشتقاقية معممة فإن U ⊆ Z (R) إذا تحقق أي من الشروط التالية : (iii) uF(v) + uv ∈ Z(R), (ii) F(uv)-vu ∈ Z(R), (i) F(uv)-uv ∈ Z(R), (iv) [F(u), v] + uv ∈ Z(R)، لكل u, v ∈ U و إذا أخدنا المجموعة الجزئية من R مثالي بدلا من مثالي لي فإننا نثبت إبدالية الحلقة الأولية.
Abstract EN
Let R be an associative prime ring, U a Lie ideal such that u2∈U for all u∈U and F : R→R be a generalized derivation.
In this paper, we show that U ⊆ Z (R) if any one of the following conditions holds: (i) F(uv) - uv∈Z(R), (ii) F(uv) - vu∈Z(R), (iii) uF(v) + uv∈Z (R), and (iv) [F(u), v] + uv∈Z(R) for all u, v∈U.
If we choose the underlying subset of R as an ideal instead of a Lie ideal of R, then we prove the commutativity of prime ring.
American Psychological Association (APA)
Bashammakh, Sabah Ahmad& Dayf, Muhammad Naji. 2014. On commutativity of prime rings with generalized derivations. Journal of King Abdulaziz University : Sciences،Vol. 26, no. 1, pp.55-65.
https://search.emarefa.net/detail/BIM-556029
Modern Language Association (MLA)
Bashammakh, Sabah Ahmad& Dayf, Muhammad Naji. On commutativity of prime rings with generalized derivations. Journal of King Abdulaziz University : Sciences Vol. 26, no. 1 (Jun. 2014), pp.55-65.
https://search.emarefa.net/detail/BIM-556029
American Medical Association (AMA)
Bashammakh, Sabah Ahmad& Dayf, Muhammad Naji. On commutativity of prime rings with generalized derivations. Journal of King Abdulaziz University : Sciences. 2014. Vol. 26, no. 1, pp.55-65.
https://search.emarefa.net/detail/BIM-556029
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 64
Record ID
BIM-556029