On the Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Rings and Some Groups of Homomorphisms
Matematičeskie zametki, Tome 101 (2017) no. 4, pp. 576-581.

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

In the present paper, we describe conditions on a vector group $C$ which are necessary and sufficient for the class of completely decomposable torsion-free Abelian groups to be a $_CEH$-class.
Keywords: completely decomposable Abelian group, group of homomorphisms, endomorphism ring, definability of Abelian groups.
@article{MZM_2017_101_4_a6,
     author = {T. A. Pushkova and A. M. Sebel'din},
     title = {On the {Definability} of {Completely} {Decomposable} {Torsion-Free} {Abelian} {Groups} by {Endomorphism} {Rings} and {Some} {Groups} of {Homomorphisms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {576--581},
     publisher = {mathdoc},
     volume = {101},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a6/}
}
TY  - JOUR
AU  - T. A. Pushkova
AU  - A. M. Sebel'din
TI  - On the Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Rings and Some Groups of Homomorphisms
JO  - Matematičeskie zametki
PY  - 2017
SP  - 576
EP  - 581
VL  - 101
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a6/
LA  - ru
ID  - MZM_2017_101_4_a6
ER  - 
%0 Journal Article
%A T. A. Pushkova
%A A. M. Sebel'din
%T On the Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Rings and Some Groups of Homomorphisms
%J Matematičeskie zametki
%D 2017
%P 576-581
%V 101
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a6/
%G ru
%F MZM_2017_101_4_a6
T. A. Pushkova; A. M. Sebel'din. On the Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Rings and Some Groups of Homomorphisms. Matematičeskie zametki, Tome 101 (2017) no. 4, pp. 576-581. http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a6/

[1] R. Baer, “Automorphism rings of primary Abelian operator groups”, Ann. of Math. (2), 44 (1943), 192–227 | DOI | MR | Zbl

[2] I. Kaplansky, “Some results on Abelian groups”, Proc. Nat. Acad. Sci. USA, 38 (1952), 538–540 | DOI | MR | Zbl

[3] A. P. Mishina, “Abelevy gruppy”, Itogi nauki i tekhn. Ser. Algebra. Topol. Geom., 10, VINITI, M., 1972, 5–45 | MR | Zbl

[4] A. M. Sebeldin, Opredelyaemost abelevykh grupp, Palmarium Acad. Publ., 2012

[5] W. May, “Endomorphisms rings of mixed Abelian groups”, Abelian Group Theory, Contemp. Math., 87, Amer. Math. Soc., Providence, RI, 1989, 61–74 | DOI | MR | Zbl

[6] A. M. Sebeldin, “Usloviya izomorfizma vpolne razlozhimykh abelevykh grupp bez krucheniya s izomorfnymi koltsami endomorfizmov”, Matem. zametki, 11:4 (1972), 403–408 | MR | Zbl

[7] L. Fuks, Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977 | MR | Zbl

[8] A. M. Sebeldin, “Gruppy gomomorfizmov vpolne razlozhimykh abelevykh grupp bez krucheniya”, Izv. vuzov. Matem., 1973, no. 7, 77–84 | MR | Zbl

[9] R. B. Warfield Jr., “Homomorphisms and duality for torsion-free groups”, Math. Z., 107:3 (1968), 189–200 | DOI | MR | Zbl

[10] K. Kuratovskii, A. Mostovskii, Teoriya mnozhestv, Mir, M., 1970 | MR