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.
ACKNOWLEDGMENTS
The author would like to give his gratitude to Shiro Goto, Yuji Kamoi, and Kazuhiko Kurano for valuable discussions and useful suggestions.
Notes
Communicated by I. Swanson.