-purity and orthogonality.
A categorical concept of completion of objects
We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.
A decomposition theorem for comodules
A Generalization of Baer's Lemma
There is a classical result known as Baer’s Lemma that states that an -module is injective if it is injective for . This means that if a map from a submodule of , that is, from a left ideal of to can always be extended to , then a map to from a submodule of any -module can be extended to ; in other words, is injective. In this paper, we generalize this result to the category consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...
A note on free regular and exact completions and their infinitary generalizations.
A Note on the Structure of Injective Diagrams.
A short proof of Eilenberg and Moore’s theorem
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
Adjoints, torsion theory and purity.
Algebraic Vector Bundles over A3 Are Trivial.
Almost free splitters
Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which are larger...
An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221)
Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if . In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.
Bounds for the homological dimensions of pullbacks.
Characterization of injective envelopes
Coherent Rings and Homologically Finite Subcategories.
Cohomología respecto a una variedad de una categoría.
Comparison of abelian categories recollements.
Componentwise injective models of functors to DGAs
The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.
Copure injective resolutions, flat resolvents and dimensions
In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize -Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring has cokernels (respectively kernels), then is -Gorenstein.
Derived functors of and abelian ab3*- and Ab4*-categories with enough injectives
Exact completion and representations in abelian categories.