Carriers of torsion-free groups
Cellular covers of cotorsion-free modules
In this paper we improve recent results dealing with cellular covers of R-modules. Cellular covers (sometimes called colocalizations) come up in the context of homotopical localization of topological spaces. They are related to idempotent cotriples, idempotent comonads or coreflectors in category theory. Recall that a homomorphism of R-modules π: G → H is called a cellular cover over H if π induces an isomorphism , where π⁎(φ) = πφ for each (where maps are acting on the left). On the one hand,...
Characterization of matrix types of ultramatricial algebras.
Characterization of the automorphisms having the lifting property in the category of Abelian -groups.
Characterization of the automorphisms of an Abelian group having the extension property. (Caractérisation des automorphismes d'un groupe abélien ayant la propriété de l'extension.)
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.
Classi di gruppi abeliani chiuse rispetto alle immagini omomorfe ed ai limiti proiettivi
Complementary permutations for abelian groups.
Complementary permutations for abelian groups. (Summary).
Computation of the mapping of factorization by the radical for of the endomorphism ring.
Cotorsion-free algebras as endomorphism algebras in - the discrete and topological cases
The discrete algebras over a commutative ring which can be realized as the full endomorphism algebra of a torsion-free -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...