Abelian Groups and Regular Modules
Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 402-411.

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

The structure of the additive group of a regular module is considered. Abelian groups that are regular modules over their rings of endomorphisms are studied. Nonreduced endoregular groups and endoregular torsion-free groups of finite rank are described.
@article{MZM_2001_69_3_a8,
     author = {P. A. Krylov and E. G. Pakhomova},
     title = {Abelian {Groups} and {Regular} {Modules}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {402--411},
     publisher = {mathdoc},
     volume = {69},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a8/}
}
TY  - JOUR
AU  - P. A. Krylov
AU  - E. G. Pakhomova
TI  - Abelian Groups and Regular Modules
JO  - Matematičeskie zametki
PY  - 2001
SP  - 402
EP  - 411
VL  - 69
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a8/
LA  - ru
ID  - MZM_2001_69_3_a8
ER  - 
%0 Journal Article
%A P. A. Krylov
%A E. G. Pakhomova
%T Abelian Groups and Regular Modules
%J Matematičeskie zametki
%D 2001
%P 402-411
%V 69
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a8/
%G ru
%F MZM_2001_69_3_a8
P. A. Krylov; E. G. Pakhomova. Abelian Groups and Regular Modules. Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 402-411. http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a8/

[1] Markov V. T., Mikhalev A. V., Skornyakov L. A., Tuganbaev A. A., “Koltsa endomorfizmov modulei i struktury podmodulei”, Itogi nauki i tekhniki. Algebra. Topologiya. Geometriya, 21, VINITI, M., 1983, 183–254

[2] Krylov P. A., “Abelevy gruppy bez krucheniya kak moduli nad svoimi koltsami endomorfizmov”, Abelevy gruppy i moduli, no. 13–14, Izd-vo TGU, Tomsk, 1996, 77–104

[3] Kash F., Moduli i koltsa, Mir, M., 1981

[4] Fuks L., Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977

[5] Richman F., Walker E. A., “Modules over PIDs that are injective over their endomorphism rings”, Ring Theory, Acad. Press, New York, 1972, 363–372 | MR

[6] Pakhomova E. G., “Abelevy gruppy kak regulyarnye moduli nad koltsami endomorfizmov”, Mezhd. konf. “Vsesibirskie chteniya po matematike i mekhanike”, T. 1, Tomsk, 1997, 32–33

[7] Feis K., Algebra: koltsa, moduli i kategorii, T. 1, Mir, M., 1977

[8] Fuks L., Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974

[9] Glaz S., Wickless W., “Regular and principal projective endomorphism rings of mixed abelian groups”, Comm. Algebra, 22:4 (1994), 1161–1176 | DOI | MR | Zbl

[10] Wickless W., “A functor from mixed groups to torsion-free groups”, Contem. Math., 171 (1995), 407–419

[11] Albrecht U. F., Goeters H. P., Wickless W., “The flat dimension of mixed abelian groups as $E$-modules”, Rocky Mount. J. Math., 25:2 (1995), 569–590 | DOI | MR | Zbl

[12] Albrecht U., “Mixed abelian groups with artinian quasi-endomorphism ring”, Comm. Algebra, 25:11 (1997), 3497–3511 | DOI | MR | Zbl

[13] Fomin A., Wickless W., “Self-small mixed abelian groups $G$ with $G/T(G)$ finite rank divisible”, Comm. Algebra, 26:11 (1998), 3563–3580 | DOI | MR | Zbl

[14] Krylov P. A., “Koltsa endomorfizmov smeshannykh abelevykh grupp”, Mezhd. konf. “Vsesibirskie chteniya po matematike i mekhanike”, T. 1, Tomsk, 1997, 20–21

[15] Warfield R. B. (Jr.), “The structure of mixed abelian groups”, Lect. Notes Math., 616, 1997, 1–38 | MR

[16] Feis K., Algebra: koltsa, moduli i kategorii, T. 2, Mir, M., 1979

[17] Arnold D. M., “Finite rank torsion-free abelian groups and rings”, Lect. Notes Math., 931, 1982 | Zbl

[18] Lambek I., Koltsa i moduli, Mir, M., 1971 | Zbl