Geodesic
Torsion-Free Abelian Groups of Finite Rank as Endomorphic Modules over Their Endomorphism Ring
Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 770-776.

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

In the paper, the additivity problem for homogeneous mappings of torsion-free Abelian groups of finite rank is solved and some close problems are considered.
Keywords: additivity problem, homogeneous mapping, torsion-free Abelian group of finite rank, near-ring, endomorphic (semi-endomorphic module), endodistributive Abelian group. 
@article{MZM_2013_94_5_a11,
     author = {D. S. Chistyakov},
     title = {Torsion-Free {Abelian} {Groups} of {Finite} {Rank} as {Endomorphic} {Modules} over {Their} {Endomorphism} {Ring}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {770--776},
     publisher = {mathdoc},
     volume = {94},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a11/}
}
TY  - JOUR
AU  - D. S. Chistyakov
TI  - Torsion-Free Abelian Groups of Finite Rank as Endomorphic Modules over Their Endomorphism Ring
JO  - Matematičeskie zametki
PY  - 2013
SP  - 770
EP  - 776
VL  - 94
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a11/
LA  - ru
ID  - MZM_2013_94_5_a11
ER  - 
%0 Journal Article
%A D. S. Chistyakov
%T Torsion-Free Abelian Groups of Finite Rank as Endomorphic Modules over Their Endomorphism Ring
%J Matematičeskie zametki
%D 2013
%P 770-776
%V 94
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a11/
%G ru
%F MZM_2013_94_5_a11
D. S. Chistyakov. Torsion-Free Abelian Groups of Finite Rank as Endomorphic Modules over Their Endomorphism Ring. Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 770-776. http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a11/

[1] P. Fuchs, C. J. Maxson, G. Pilz, “On rings for which homogeneous maps are linear”, Proc. Amer. Math. Soc., 112:1 (1991), 1–7 | DOI | MR | Zbl

[2] J. Hausen, J. A. Johnson, “Centralizer near-rings that are rings”, J. Austral. Math. Soc. Ser. A, 59:2 (1995), 173–183 | DOI | MR | Zbl

[3] A. B. van der Merwe, “Unique addition modules”, Comm. Algebra, 27:9 (1999), 4103–4115 | DOI | MR | Zbl

[4] M. Dugas, C. J. Maxson, “Quasi-E-locally cyclic torsion-free abelian groups”, Proc. Amer. Math. Soc., 133:12 (2005), 3447–3453 | DOI | MR | Zbl

[5] D. S. Chistyakov, O. V. Lyubimtsev, “Abelevy gruppy kak endomorfnye moduli nad svoim koltsom endomorfizmov”, Fundament. i prikl. matem., 13:1 (2007), 229–233 | MR | Zbl

[6] O. V. Lyubimtsev, D. S. Chistyakov, “Abelevy gruppy kak $\mathrm{UA}$-moduli nad koltsom $\mathbb Z$”, Matem. zametki, 87:3 (2010), 412–416 | DOI | MR | Zbl

[7] D. S. Chistyakov, “Endomorfnye nerazlozhimye abelevy gruppy bez krucheniya ranga 3”, Vestn. Tomsk. gos. un-ta. Matem., mekh., 13:1 (2011), 61–66

[8] A. A. Tuganbaev, Teoriya kolets. Arifmeticheskie moduli i koltsa, MTsNMO, M., 2009

[9] P. A. Krylov, A. V. Mikhalev, A. A. Tuganbaev, Abelevy gruppy i ikh koltsa endomorfizmov, Faktorial, M., 2006

[10] L. Fuks, Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974 ; Л. Фукс, Бесконечные абелевы группы, Т. 2, Мир, М., 1977 | MR | Zbl | MR | Zbl

[11] E. V. Tarakanov, “Endodistributivnye moduli nad dedekindovymi koltsami”, Abelevy gruppy i moduli, 9, Tomsk. un-t, Tomsk, 1990, 106–115 | MR | Zbl

[12] M. A. Turmanov, “Endochistye podmoduli abelevykh grupp bez krucheniya ranga 2”, Abelevy gruppy i moduli, 9, Tomsk. un-t, Tomsk, 1990, 119–124 | MR | Zbl