The technique of Bourbaki sequences is used in  in order to study the graded maximal Cohen‐Macaulay modules of rank two over the singularity x31+x32+x33+x34. 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 x31+x32+x33+x34.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 email@example.com
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 firstname.lastname@example.org