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Let  K  be a field of characteristic zero. We show that the image of a linear  K -derivation of rank less than or equal to two over the polynomial algebrais a Mathieu-Zhao subspace. We have further shown that, under certain conditions, the image of-derivations ofis a Mathieu-Zhao subspace.

communications in algebra

Image of linear  K -derivations and linear ΚƐ-derivations of  K [ x                  1 , x                  2 , x                  3 , x                  4 ]