In this paper, the notion of cotorsion classes is introduced into higher homological algebra . Our results motivate definition, showing that n -cotorsion satisfies usual properties one could expect. particular, a version Wakamatsu's Lemma proved. At last section, connections with wide subcategories are studied.

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...

Let R be a ring and T be a 1-tilting right R-module. Then T is of countable type. Moreover, T is of finite type in case R is a Prüfer domain.

Abstract We show that a direct limit of projective contramodules (over right linear topological ring) is if it has cover. A similar result obtained for $\infty $-strictly flat dimension not exceeding $1$, using an argument based on the notion Jacobson radical. Covers and precovers limits more general classes objects, both in abelian categories with exact nonexact limits, are also discussed, eye...

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.