Abstract
We introduce a notion of Gorenstein R -algebras over a commutative Gorenstein ring R . Then we provide a necessary and sufficient condition for a tilting complex over a Gorenstein R -algebra A to have a Gorenstein R -algebra B as the endomorphism algebra and a construction of such a tilting complex. Furthermore, we provide an example of a tilting complex over a Gorenstein R -algebra A whose endomorphism algebra is not a Gorenstein R -algebra.
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