The technique of Bourbaki sequences is used in [4] in order to study the graded maximal Cohen-Macaulay modules of rank two over the singularity x_1~3 + x_2~3 + x_3~3 + x_4~3. In the second section of this paper we complete a small gap in the classification of these modules which are non-orientable. In the last section we give a brief survey on the classification of the graded non-orientable maximal Cohen-Macaulay modules of rank two over x_1~3 + x_2~3 + x_3~3 + x_4~3.
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