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Let K be a field of characteristic zero. We prove that images of a linearK-derivation and a linear K-E-derivation of the ring K[x 1 ,x 2 ,x 3 ] ofpolynomial in three variables over K are Mathieu-Zhao subspaces, which affirmsthe LFED conjecture for linear K-derivations and linear K-E-derivations of K[x1 ,x 2 ,x 3 ].

Images of Linear Derivations and Linear E-derivations of K[x 1 ,x 2 ,x 3 ]