Characterization of the inessential endomorphisms in the category of Abelian groups. (English) Zbl 1061.20047

Abdelalim, S.; Essannouni, H.

Publ. Mat., Barc. 47, No. 2, 359-372 (2003).

An endomorphism \(f\) of an Abelian group \(A\) is said to be inessential (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 it is shown that \(f\) is inessential if and only if \((f-v\cdot\text{id}_A)(A)\) is contained in the maximal divisible subgroup of \(A\) for some \(v\in\mathbb{Z}\).

Reviewer: Grigore Călugăreanu (Safat)

MSC:

20K30	Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
20K40	Homological and categorical methods for abelian groups
20K27	Subgroups of abelian groups

Keywords:

inessential endomorphisms; categories of Abelian groups; maximal divisible subgroups