Acta mathematica scientia, Series B >
LIE IDEALS, MORITA CONTEXT AND GENERALIZED (α, β)-DERIVATIONS
Received date: 2012-05-16
Revised date: 2012-10-05
Online published: 2013-07-20
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.
S. Khalid NAUMAN , Nadeem ur REHMAN , R. M. AL-OMARY . LIE IDEALS, MORITA CONTEXT AND GENERALIZED (α, β)-DERIVATIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(4) : 1059 -1070 . DOI: 10.1016/S0252-9602(13)60063-6
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