For a module-finite algebra over commutative noetherian ring, we give complete description of flat cotorsion modules in terms prime ideals the algebra, as generalization Enochs' result for ring. As consequence, show that pointwise Matlis duality gives bijective correspondence between isoclasses indecomposable injective left and right modules. This is an explicit realization Herzog's homeomorphi...

We study ideal cotorsion pairs associated to almost exact structures in extension closed subcategories of triangulated categories. This approach allows us extend the recent approximation theory developed by Fu, Herzog et al. for categories above mentioned context. In last part paper we apply order projective classes (in particular localization or smashing subcategories) compactly generated