Let ▫$L$▫ be a Lie algebra and let ▫$A$▫ be an associative commutative algebra with unity, both over the same field ▫$F$▫. We consider the following question. Is every generalized derivation (resp. ...quasiderivation) of ▫$L \otimes A$▫ the sum of a derivation and a map from the centroid of ▫$L \otimes A$▫, if the same holds true for ▫$L$▫?
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