دراسة S – خاصة أصلية في صف جبور لي
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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