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We generalize the results of Leger and Luks, Zhang R. and Zhang Y.; Chen, Ma, Ni, Niu, Zhou and Fan; Kaygorodov and Popov about generalized derivations of color n-ary algebras to the case of n-ary Hom- Omega color algebras. Particularly, we prove some properties of generalized derivations of multiplicative n-ary Hom- Omega color algebras. Moreover, we prove that the quasiderivation algebra of any multiplicative n-ary Hom-Omega color algebra can be embedded into the derivation algebra of a larger multiplicative n-ary Hom- Omega color algebra.
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Generalized derivation Color algebra Hom-algebra Hom–Lie superalgebra n-ary algebra