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Cellular covers of cotorsion-free modules

Rüdiger Göbel, José L. Rodríguez, Lutz Strüngmann (2012)

Fundamenta Mathematicae

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 π ⁎ : H o m R ( G , G ) ≅ H o m R ( G , H ) , where π⁎(φ) = πφ for each φ ∈ H o m R ( G , G ) (where maps are acting on the left). On the one hand,...

Characterization of the inessential endomorphisms in the category of Abelian group.

S. Abdelalim, H. Essannouni (2003)

Publicacions Matemàtiques

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.

Cotorsion-free algebras as endomorphism algebras in L - the discrete and topological cases

Rüdiger E. Göbel, Brendan Goldsmith (1993)

Commentationes Mathematicae Universitatis Carolinae

The discrete algebras A over a commutative ring R which can be realized as the full endomorphism algebra of a torsion-free R -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, V = L . 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...

Endomorphism algebras over large domains

Rüdiger Göbel, Simone Pabst (1998)

Fundamenta Mathematicae

The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain

Endomorphism kernel property for finite groups

Heghine Ghumashyan, Jaroslav Guričan (2022)

Mathematica Bohemica

A group G has the endomorphism kernel property (EKP) if every congruence relation θ on G is the kernel of an endomorphism on G . In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.

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