Rings in which derivations satisfy certain algebraic conditions

Abstract

The primary purpose of this paper is to investigate some commutator conditions for rings, which were suggested by group-theoretic results of F, W. Levi, I. D. Macdonald and N. D. Gupta. Most of these conditions can be simply interpreted in terms of inner derivations, and they suggest further questions about arbitrary derivations.In

Commutativity results for semiprime rings with derivations

“…This result yielded a result of Bell and Kappe [4]. We also studied derivations d satisfying d(xy) d(yx) for all x,y U.…”

The k-Derivation Acting as a k-Endomorphism and as an Anti-k-Endomorphism on Semiprime Nobusawa Gamma Ring

“…In classical ring theory, H. E. Bell and L. C. Kappe [4] proved that if d is a derivation of a semiprime ring R which is either an endomorphism or an anti-endomorphism on R, then 0…”

Generalized Derivations Acting as Homomorphisms and Anti-Homomorphisms on Lie Ideals of Prime Rings

“…In [2], Bell and Kappe prove that if a derivation acts as a homomorphism and as an anti-homomorphism on a non-zero ideal I of a prime ring R, then 0  d . Asma, Rehman and Shakir [1] extend this result to a square closed Lie ideal, whereas Rehman [8] proves the same result for generalized derivations.…”