Abstract
Abstract Let A and B be two associative rings, let I be an ideal of B and let f ∈ Hom ( A , B ) {f\in\mathrm{Hom}(A,B)} . In this paper, we give a complete description of generalized derivations over A ⋈ f I {A\bowtie^{f}I} . Furthermore, when A is prime or semi-prime, we give several identities on generalized derivations which provide the commutativity of A ⋈ f I {A\bowtie^{f}I} .
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