Connected Graded Algebra Projection Module Category Triangular Structure

This Master degree thesis is on triangulated structure of the category of projective modules over a connected graded algebra. Firstly, we generalize the characterization of Quasi-Frobenius ring to the graded case. Then we give a characterization of the connected graded algebra, for which the category of projective modules admits a triangulation. Con-versely, we construct a triangulated structure of the category of projective modules under some assumptions on the connected graded algebra. Besides, we prove a one to one corre-spondence between the set of all the triangulated structures of the category of projective modules and the set of nonzero elements in k. Finally, the categories, of projective mod-ules, with different triangulated structure are triangulated equivalent.