Let A be an integral domain and K its field of fractions. An A-module E is said to be torsion
free if ax= 0 for azA, x EE implies a= 0 or x= 0. We will say that a submodule E1 of an A …

We prove general results about completeness of cotorsion theories and existence of covers
and envelopes in locally presentable abelian categories, extending the well-established …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

Homological algebra had its origins in the 19th century, via the work of Riemann (1857) and
Betti (1871) on “homology numbers,” and the rigorous development of the notion of …

Many branches of algebra are linked by the theory of modules. Since the notion of a module
is obtained essentially by a modest generalisation of that of a vector space, it is not …

Abstract Contents Introduction § 1. Projectively generated proper classes § 2. Projective
proper classes § 3. Injectively generated and injective proper classes § 4. Spectral …

We consider the homotopy category of complexes of projective modules over a Noetherian
ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic …

Tilting complexes, pe categories and reck derived module categories o rings Page 1
Journal of Pure and Applied ,?Igebra 73 ( 1991) l’ I I-232 North-Holland 211 Tilting …

In the general setting of Grothendieck categories with enough projectives, we prove
theorems that make possible to restrict the study of the problem of the existence of F-covers …

A Serre class in an abelian category is a nonempty subclass J> of cĄ closed under
subobjects, quotient objects, and extensions. Th importance of such classes stems from the …