- Cotorsion modules
A module M is called cotorsion if for all flat modules X, $Ext_R^1(X,M)=0$ .
- Strongly cotorsion modules
M is called strongly cotorsion if for all modules X of finite flat dimension, $Ext_R^1(X,M)=0$ .
By definitions it is easy to observe that strongly cotorsion modules are cotorsion modules. But I fail to find some examples to show the two classes are different. Furthermore, what happens when the Ext functor is replace by the Tor functor?