دراسة S – خاصة أصلية في صف جبور لي

Authors

  • أحمد الغصين

Abstract

هذا البحث مكرس للإجابة على السؤال التالي :

ليكن L جبر لي فوق حقل مميزه يساوي الصفر  ولتكن S –خاصة أصلية في صف جبور لي .

هل S-خاصة أصلية تكون دوما مثالية مميزة في الجبر L ؟

للإجابة على هذا السؤال عرضنا أولا بعض التعريفات والمبرهنات  والتمهيدات الضرورية ومن ثم برهنا أنه اذا كان   D أي اشتقاق في جبر لي  L   بحيث أن n D(S(L))n Í   S(L)  حيث n اكبر او تساوي الواحد عندئذ D(S(L)) Í   S(L)  وكذلك بينا انه من اجل أي جبر ارتيني     S(L) هي مثالية مميزة في L . وبعد ذلك اعطينا مثالا  يجيب على  السؤال الطروح , إذ ليس من الضروري أن تكون S دوما مثالية مميزة في L .

In this paper we answer of the following question . Let L be a Lie algebra over a field K with characteristic zero and let S(L) be a S-radical property of L Is this S(L) is characteristic ideal in L ?

For this reason first we proved, if D is any derivation of Lie algebra L such that D(S(L) n) Í S(L)n , for some n ³ 1 , then D(S(L) ) Í S(L) , moreover , for every  Artinian algebra L  its radical S(L) is characteristic ideal in L.Next  we gave an example  which gave a negative solution for above question .

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Published

2018-11-29

How to Cite

1.
الغصين أ. دراسة S – خاصة أصلية في صف جبور لي. TUJ-BA [Internet]. 2018Nov.29 [cited 2024May2];24(2). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/4904

Issue

Vol. 24 No. 2 (2002): العلوم الأساسية

Section

Articles

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