Abstract
Let R be a commutative ring, 𝒞 be a semidualizing R-module. We show that the Auslander class 𝒜𝒞(R) with respect to 𝒞 is the first left orthogonal class of some pure injective module M, that is, 𝒜𝒞(R) =⊥1 M, and the Bass class ℬ𝒞(R) is the first right orthogonal class of some G 𝒞-projective module N, that is, ℬ𝒞(R) = N ⊥1 . As applications, we can see that (𝒜𝒞(R), 𝒜𝒞(R)⊥) is a cotorsion theory generated by a set. Especially, we show that (⊥ℬ𝒞(R), ℬ𝒞(R)) is a complete hereditary cotorsion theory cogenerated by a set.
ACKNOWLEDGMENTS
The authors would like to express their sincere thanks to the referee for his or her careful reading of the manuscript and helpful suggestions.
This research was partially supported by the National Natural Science Foundation of China (No. 10971090).
Notes
Communicated by I. Swanson.