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Abstract
The purpose of this paper is to connect the notion of Gorenstein dimension with AS-Gorenstein algebras. In particular, we show that a noetherian connected graded algebra having a balanced dualizing complex is AS-Gorenstein if the balanced dualizing complex has finite Gorenstein dimension. As a preparation, we generalize the Auslander–Bridger formula to the class of noncommutative noetherian connected graded algebras having balanced dualizing complexes.
ACKNOWLEDGMENT
The author would like to give his deep gratitude to Izuru Mori for a lot of valuable discussions and helpful suggestions.
Notes
Communicated by Q. Wu.