Cartan-Eilenberg projective, injective and flat complexes
Let be an associative ring with identity and a class of -modules. In this article: we first give a detailed treatment of Cartan-Eilenberg complexes and extend the basic properties of the class to the class ). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these complexes,...