Study on triangulated categories and its application to Cohen-Macaulay modules

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In order to analyze the degeneration of Cohen-Macaulay modules, we have given careful consideration to the analogue of degeneration in the stable category, which we call the stable degeneration. As a result we obtained several satisfactory results which clarify the degeneration over a simple singularity.Moreover, about a finitely generated module over a complete local ring of prime characteristic, we gave a proof of the duality theorem between the left Frobenius actions on a module and the right Frobenius actions on its Matlis dual module.