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

We discuss the topic of full transitivity cotorsion hull a separable p-group. This plays significant role in description lattice fully invariant subgroups group. A condition is established, fulfillment which makes not transitive.

We study the properties of rings satisfying Auslander-type conditions. If an artin algebra Λ satisfies the Auslander condition (that is, Λ is an ∞-Gorenstein artin algebra), then we construct two kinds of subcategories which form functorially finite cotorsion theories. Noetherian rings satisfying ‘Auslander-type conditions’ on self-injective resolutions can be regarded as certain non-commutativ...