Torsion-free Abelian groups of finite rank with marked bases
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 201-228.

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

We define a one-to-one correspondence between torsion-free Abelian groups of finite rank with marked bases and finite sequences of elements of finitely presented modules over the ring of polyadic numbers. This correspondence is a duality of two categories.
@article{FPM_2019_22_4_a13,
     author = {A. A. Fomin},
     title = {Torsion-free {Abelian} groups of finite rank with marked bases},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {201--228},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a13/}
}
TY  - JOUR
AU  - A. A. Fomin
TI  - Torsion-free Abelian groups of finite rank with marked bases
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2019
SP  - 201
EP  - 228
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a13/
LA  - ru
ID  - FPM_2019_22_4_a13
ER  - 
%0 Journal Article
%A A. A. Fomin
%T Torsion-free Abelian groups of finite rank with marked bases
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2019
%P 201-228
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a13/
%G ru
%F FPM_2019_22_4_a13
A. A. Fomin. Torsion-free Abelian groups of finite rank with marked bases. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 201-228. http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a13/

[1] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR

[2] Leng S., Algebra, Mir, M., 1968

[3] Maltsev A. I., “Abelevy gruppy konechnogo ranga bez krucheniya”, Matem. sb., 4:1 (1938), 45–68 | Zbl

[4] Fomin A. A., “K teorii faktorno delimykh grupp. 1”, Fundament. i prikl. matem., 17:8 (2012), 153–167

[5] Fomin A. A., “K teorii faktorno delimykh grupp. 2”, Fundament. i prikl. matem., 20:5 (2015), 157–196

[6] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974; v. 2, 1977

[7] Baer R., “Abelian groups without elements of finite order”, Duke Math. J., 3 (1937), 68–122 | MR

[8] Beaumont R. A., Pierce R. S., Torsion Free Groups of Rank Two, Mem. Amer. Math. Soc., 38, 1961 | MR | Zbl

[9] Derry D., “Über eine Klasse von abelschen Gruppen”, Proc. London Math. Soc., s2-43 (1938), 490–506 | MR

[10] Fomin A. A., “Finitely presented modules over the ring of universal numbers”, Abelian Group Theory and Related Topics, Contemp. Math., 171, Amer. Math. Soc., Providence, 1994, 109–120 | MR | Zbl

[11] Fomin A., “Invariants for Abelian groups and dual exact sequences”, J. Algebra, 322:7 (2009), 2544–2565 | MR | Zbl

[12] Fomin A. A., Wickless W. J., “Quotient divisible Abelian groups”, Proc. Amer. Math. Soc., 126:1 (1998), 45–52 | MR | Zbl

[13] Kurosh A. G., “Primitive torsionsfreie abelsche Gruppen von endlichen Range”, Ann. Math., 38 (1937), 175–203 | MR | Zbl

[14] Levi F., Abelsche Gruppen mit abzahlbaren Elementen, Habilitationsschrift, Leipzig, 1917

[15] Pontryagin L. S., “The theory of topological commutative groups”, Ann. Math., 13 (1934), 361–388 | MR