On n-commuting and n-skew-commuting maps with generalized derivations in prime and semiprime rings |
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| Authors: | N. ur Rehman V. De Filippis |
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| Affiliation: | 1.Aligarh Muslim University,Aligarh,India;2.University of Messina,Messina,Italy |
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| Abstract: | Let R be a ring with center Z(R), let n be a fixed positive integer, and let I be a nonzero ideal of R. A mapping h: R → R is called n-centralizing (n-commuting) on a subset S of R if [h(x),x n ] ∈ Z(R) ([h(x),x n ] = 0 respectively) for all x ∈ S. The following are proved: | (1) | if there exist generalized derivations F and G on an n!-torsion free semiprime ring R such that F 2 + G is n-commuting on R, then R contains a nonzero central ideal |
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