Abstract
Let [Formula: see text] be a prime or semiprime ring, [Formula: see text] a nonzero left-sided ideal of [Formula: see text] and [Formula: see text] be two automorphisms of [Formula: see text]. Let [Formula: see text] and [Formula: see text] be two generalized [Formula: see text]-derivations of [Formula: see text] associated with [Formula: see text]-derivations [Formula: see text] and [Formula: see text], respectively. The purpose of this paper is to investigate the following identities: (1) [Formula: see text]; (2) [Formula: see text]; (3) [Formula: see text]; (4) [Formula: see text]; (5) [Formula: see text]; (6) [Formula: see text]; (7) [Formula: see text]; (8) [Formula: see text]; (9) [Formula: see text]; (10) [Formula: see text]; (11) [Formula: see text]; (12) [Formula: see text], for all [Formula: see text].
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