… the little finitistic dimension of R. We show that FindimR < ∞ if and only if the following
dimensions are finite for some cotorsion pair (A,B) in ModR: the relative projective dimension of A …

… If A contains a generator of finite projective dimension then we have the obvious dual … a
generator of finite projective dimension then (⊥(ex B), ex B) is a cotorsion pair. For the proof we …

… dimension of complexes with respect to the cotorsion pair (𝒳,𝒴), and give a construction of
Tate 𝒳-resolution of complexes of finite 𝒢(𝒳)-resolution dimensions. … homological dimensions …

… notion, that of Gorenstein injective dimension of complexes over arbitrary associative rings.
… study of homological dimensions of complexes of R-modules related to a cotorsion pair (A, B…

… More precisely our results give a classification of all cotorsion pairs (A, y) in an abelian …
classifications of cotorsion pairs and cotorsion triples in an abelian category and torsion pairs in a …

… We use isomorphisms of homology, while Qi used isomorphisms in the stable category of
H-… We may also define a Hopfological analogue of this construction by using a cotorsion pair. …

… a more general setting involving two special cotorsion pairs of modules. … cotorsion pair is
the flat cotorsion pair (ℱ,𝒞) in Mod−R. The book [11] is a standard reference for cotorsion pairs. …

… dimensions. The above equational approach leads to a description of the first singular
homology … on groups of cohomological dimension 1, we calculate the first homology groups of …

… homological dimensions for modules over the rings R and H, as well as the dimension of the
category of cotorsion … we find that the dimension of $ is equal to the global dimension of R. …

… to define Gorenstein homological dimensions and … cotorsion pairs and approximations. In
recent years, a powerful machinery for producing approximations via complete cotorsion pairs …