| LIE IDEALS, MORITA CONTEXT AND GENERALIZED （α β）-DERIVATIONS |
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| 作者姓名： | S. Khalid NA UMAN Nadeem ur REHMAN R. M. AL-OMARY |
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| 作者单位： | [1]Department of Mathematics, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia [2]Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India [3]Department of Mathematics, Ibb University, Ibb, Yemen |
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| 摘 要： | A classical problem in ring theory is to study conditions under which a ring is forced to become commutative. Stimulated from Jacobson＇s famous result, several tech- niques are developed to achieve this goal. In the present note, we use a pair of rings, which are the ingredients of a Morita context, and obtain that if one of the ring is prime with the generalized （α β）-derivations that satisfy certain conditions on the trace ideal of the ring, which by default is a Lie ideal, and the other ring is reduced, then the trace ideal of the reduced ring is contained in the center of the ring. As an outcome, in case of a semi-projective Morita context, the reduced ring becomes commutative.
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| 关 键 词： | Lie理想 广义 Morita关系 高科技技术 理想环 跟踪 素数 |
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