A characterization of countable Butler groups
A characterization of Ext(G,ℤ) assuming (V = L)
We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence of cardinals satisfying (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that equals the p-rank of Ext(G,ℤ) for every...
A closed category of reflexive topological abelian groups
A Generalization of Baer's Splitting problem on Abelian groups.
A homological algebra for valuated groups
A note on coflat abelian groups
A note on the countable extensions of separable -projective abelian -groups
It is proved that if is a pure -projective subgroup of the separable abelian -group for such that , then is -projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).
-projective resolutions and an Azumaya theorem for a class of mixed abelian groups
A remark on subgroups of infinite index in Poincaré duality groups.
A useful category for mixed Abelian groups.
Abelian group extensions and the axiom of constructibility.
Abelian group pairs having a trivial coGalois group
Torsion-free covers are considered for objects in the category Objects in the category are just maps in -Mod. For we find necessary and sufficient conditions for the coGalois group associated to a torsion-free cover, to be trivial for an object in Our results generalize those of E. Enochs and J. Rado for abelian groups.
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.
Algebraic Classes of Abelian Torsion-Free and Lattice-Ordered Groups
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...
Almost-flat modules
We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of -static modules is closed under the kernels.
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.
Characterization of the automorphisms having the lifting property in the category of Abelian -groups.
Characterization of the inessential endomorphisms in the category of Abelian group.
An endomorphism f of an Abelian group A is said to be inessentia! (in the category of Abelian groups) if it can be extended to an endomorphism of any Abelian group which contains A as a subgroup. In this paper we show that f is as above if and only if (f - v idA)(A) is contained in the rnaximal divisible subgroup of A for some v belonging to Z.
Clones of spaces and maps in homotopy theory.