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On commutativity of rings with generalized derivations

Authors :
Nadeem ur Rehman
Mohd Arif Raza
Tarannum Bano
Source :
Journal of the Egyptian Mathematical Society, Vol 24, Iss 2, Pp 151-155 (2016)
Publication Year :
2016
Publisher :
SpringerOpen, 2016.

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)∘md(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.

Details

Language :
English
ISSN :
1110256X
Volume :
24
Issue :
2
Database :
Directory of Open Access Journals
Journal :
Journal of the Egyptian Mathematical Society
Publication Type :
Academic Journal
Accession number :
edsdoj.3b3d2f7ffdbb4bc49373ef47635aa196
Document Type :
article
Full Text :
https://doi.org/10.1016/j.joems.2014.12.011