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LIE IDEALS, MORITA CONTEXT AND GENERALIZED (α, β)-DERIVATIONS

Authors
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jul 30, 2013
Volume
33
Issue
4
Pages
1059–1070
Source
MyScienceWork
License
White

Abstract

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 techniques 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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