Given two finite dimensional algebras $A$ and $B$ over a field. The Gorenstein dimension of an algebra A is defined as the injective dimension of the module A. The finitistic dimension of an algebra A is defined as the supremum of projective dimensions of modules having finite projective dimension.
Are there exact formulas for the Gorenstein dimension and finitistic dimension of $A \otimes\_K B$? I found that: <http://at.yorku.ca/c/a/f/e/49.htm> but no related paper at the moment. Im looking for a reference to quote if possible.



Homological dimensions of tensor products of algebras
For the finitistic dimension, this is Theorem 16 in


*Samuel Eilenberg, Alex Rosenberg, and Daniel Zelinsky*, MR 98774 [**On the dimension of modules and algebras. VIII. Dimension of tensor products**](http://www.ams.org/mathscinet-getitem?mr=98774), *Nagoya Math. J.* **12** (1957), 71--93.


