Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings

Let R be a prime ring with characteristic different from 2 , let U be its right Utumi quotient ring, let C be its extended centroid, let F and G be additive maps on R , let f ( x 1 , . . . ,x n ) be a multilinear polynomial over C , and let I be a nonzero right ideal of R . We obtain information abo...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2016-07, Vol.68 (2), p.203-223
Main Authors: De Filippis, V., Dhara, B., Scudo, G.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Polynomials
Statistics
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Summary:Let R be a prime ring with characteristic different from 2 , let U be its right Utumi quotient ring, let C be its extended centroid, let F and G be additive maps on R , let f ( x 1 , . . . ,x n ) be a multilinear polynomial over C , and let I be a nonzero right ideal of R . We obtain information about the structure of R and describe the form of F and G in the following cases: [( F 2 + G )( f ( r 1 , . . . , r n )) , f ( r 1 , . . . , r n )] = 0 for all r 1 , . . . , r n ∈ R , where F and G are generalized derivations of R ; [( F 2 + G )( f ( r 1 , . . . , r n )) , f ( r 1 , . . . , r n )] = 0 for all r 1 , . . . , r n ∈ I , where F and G are derivations of R .
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-016-1219-0