Geodesic
Abelian groups with monomorphisms invariant with respect to epimorphisms
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2018), pp. 86-93

Voir la notice de l'article provenant de la source Math-Net.Ru

If for any injective endomorphism $\alpha$ and surjective endomorphism $\beta$ of abelian group there exist its endomorphism $\gamma$ such that $\beta\alpha=\alpha\gamma$ ($\alpha\beta=\gamma\alpha$, respectively), then such a property of the group is called $R$-property ($L$-property, respectively). It is shown that if reduced torsion-free group possesses $R$- or $L$-property, then endomorphism ring of a group is normal. We describe the divisible groups and direct sums of cyclic groups with $R$- or $L$-property.
Mots-clés : injective endomorphism
Keywords: surjective endomorphism, normal endomorphism ring. 
@article{IVM_2018_12_a5,
     author = {A. R. Chekhlov},
     title = {Abelian groups with monomorphisms invariant with respect to epimorphisms},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--93},
     publisher = {mathdoc},
     number = {12},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_12_a5/}
}
TY  - JOUR
AU  - A. R. Chekhlov
TI  - Abelian groups with monomorphisms invariant with respect to epimorphisms
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 86
EP  - 93
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_12_a5/
LA  - ru
ID  - IVM_2018_12_a5
ER  - 
%0 Journal Article
%A A. R. Chekhlov
%T Abelian groups with monomorphisms invariant with respect to epimorphisms
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 86-93
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2018_12_a5/
%G ru
%F IVM_2018_12_a5
A. R. Chekhlov. Abelian groups with monomorphisms invariant with respect to epimorphisms. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2018), pp. 86-93. http://geodesic.mathdoc.fr/item/IVM_2018_12_a5/