Abstract We present the concept of cotorsion pairs cut along subcategories an abelian category. This provides a generalization complete pairs, and represents general framework to find approximations restricted certain subcategories. also exhibit some connections between Auslander–Buchweitz approximation theory, by considering relative analogs for Frobenius contexts. Several applications are giv...

We describe a general construction of a module A from a given module B such that Ext(B,A) = 0 and we apply it to answer several questions on splitters, cotorsion theories, and saturated rings.

The notion of extriangulated category was introduced by Nakaoka and Palu giving a simultaneous generalization exact categories triangulated categories. Our first aim is to provide an extension Auslander's formula: for some $\mathcal{C}$, there exists localization sequence $\operatorname{def}\mathcal{C} \to \mod\mathcal{C} \operatorname{lex}\mathcal{C}$, where $\operatorname{lex}\mathcal{C}$ den...

In this paper, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.

In this paper, we study (complete) cotorsion pairs in extriangulated categories. First, a relationship between an interval of the poset and coheart associated to interval. Secondly, establish bijection bounded hereditary silting subcategories