Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

In this paper we introduce and study the weak Gorenstein global dimension of a ring $ R $
with respect to a left $ R $-module $ C $. We provide several characterizations of when this …

We present the concept of cotorsion pairs cut along subcategories of an abelian category.
This provides a generalization of complete cotorsion pairs, and represents a general …

Let 𝒟 be either the category of R-modules or the category of chain complexes of R-modules
and ℳ a cofibrantly generated hereditary abelian model structure on 𝒟. First, we get a new …

Notes on resolving resolution dimensions Page 1 Journal of Algebra and Its Applications Vol.
21, No. 10 (2022) 2250194 (9 pages) c World Scientific Publishing Company DOI: 10.1142/S0219498822501948 …

Abstract Let XX, UU and ZZ be classes of left R-modules, WW be a class of right R-modules
and X ⊆ UX⊆ U. In this paper, we investigate the relationship between Z Z-proper (resp. Z Z …