ABSTRACT
Let R be an artin algebra. We prove that a tilting R-module ω is cotilting if and only if every finitely generated R-module has finite ω-Gorenstein resolution dimension and that a cotilting R-module ω is tilting if and only if every finitely generated R-module has finite ω-Gorenstein coresolution dimension.
ACKNOWLEDGMENT
The author was supported by the National Natural Science Foundation of China.
Notes
#Communicated by B. H. Zimmermann.