On G-Regular Local Rings |
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| Authors: | Ryo Takahashi |
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| Institution: | 1. Department of Mathematical Sciences, Faculty of Science , Shinshu University , Matsumoto, Nagano, Japan takahasi@math.shinshu-u.ac.jp |
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| Abstract: | In this article, we define a G-regular local ring as a commutative, noetherian, local ring, over which all totally reflexive modules are free. We study G-regular local rings and observe that they behave similarly to regular local rings. We extend Eisenbud's matrix factorization theorem and Knörrer's periodicity theorem to G-regular local rings. |
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| Keywords: | G-dimension G-regular local ring Knörrer's periodicity Matrix factorization Totally reflexive module |
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