On commutativity of rings with generalized derivations | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 24, Issue 2, 2016, Pages 151-155 PDF (341.48 K) | ||
| DOI: 10.1016/j.joems.2014.12.011 | ||
| Authors | ||
| Nadeem ur Rehman; Mohd Arif Raza; Tarannum Bano | ||
| Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India | ||
| Abstract | ||
| Let R be a prime ring, extended centroid C , Utumi quotient ring U , and m, n ≥ 1 are fixed positive integers, F a generalized derivation associated with a nonzero derivation d of R . We study the case when one of the following holds: (i) F (x ) ◦m d(y ) = (x ◦ y ) n and (ii) (F (x ) ◦ d(y )) m = (x ◦ y ) n , for all x, y in some appropriate subset of R . We also examine the case where R is a semiprime ring. | ||
| Keywords | ||
| Prime and semiprime rings; Generalized derivations; Martindale ring of quotients; Generalized polynomial identity (GPI); Ideal | ||
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