Geodesic
Rings whose $p$-ranks do not exceed 1
Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 476-487 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider associative torsion-free rings of finite rank whose $p$-ranks do not exceed 1. For these rings, certain analogues of Wedderburn's theorem on finite-dimensional algebras are found. Bibliography: 11 titles.
Keywords: associative ring, mixed Abelian group, ring of polyadic numbers, $p$-rank, $E$-ring.
Mots-clés : quotient-divisible group 
@article{SM_2014_205_4_a1,
     author = {O. Guseva and A. V. Tsarev},
     title = {Rings whose $p$-ranks do not exceed~1},
     journal = {Sbornik. Mathematics},
     pages = {476--487},
     year = {2014},
     volume = {205},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_4_a1/}
}
TY  - JOUR
AU  - O. Guseva
AU  - A. V. Tsarev
TI  - Rings whose $p$-ranks do not exceed 1
JO  - Sbornik. Mathematics
PY  - 2014
SP  - 476
EP  - 487
VL  - 205
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_2014_205_4_a1/
LA  - en
ID  - SM_2014_205_4_a1
ER  - 
%0 Journal Article
%A O. Guseva
%A A. V. Tsarev
%T Rings whose $p$-ranks do not exceed 1
%J Sbornik. Mathematics
%D 2014
%P 476-487
%V 205
%N 4
%U http://geodesic.mathdoc.fr/item/SM_2014_205_4_a1/
%G en
%F SM_2014_205_4_a1
O. Guseva; A. V. Tsarev. Rings whose $p$-ranks do not exceed 1. Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 476-487. http://geodesic.mathdoc.fr/item/SM_2014_205_4_a1/

[1] I. A. Aleksandrov, P. A. Krylov, “F. E. Molin – uchenyi i pedagog”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2011, no. 3, 6–11

[2] R. A. Beaumont, R. S. Pierce, “Torsion free rings”, Illinois J. Math., 5:1 (1961), 61–98 | MR | Zbl

[3] A. V. Tsarev, “Pure subrings of the rings $\mathbb Z_\chi$”, Sb. Math., 200:9-10 (2009), 1537–1563 | DOI | DOI | MR | Zbl

[4] O. I. Davydova, “Rank-$1$ quotient divisible groups”, J. Math. Sci., 154:3 (2008), 295–300 | DOI | MR | Zbl

[5] E. A. Timoshenko, “Base fields of $\mathrm{csp}$-rings”, Algebra and Logic, 49:4 (2010), 378–385 | DOI | MR | Zbl

[6] L. Fuchs, Infinite abelian groups, v. I, II, Pure Appl. Math., 36, Academic Press, New York–London, 1970, 1973, xi+290 pp., ix+363 pp. | MR | MR | MR | MR | Zbl | Zbl

[7] P. A. Krylov, A. V. Mikhalev, A. A. Tuganbaev, Abelevy gruppy i ikh koltsa endomorfizmov, Faktorial Press, M., 2006, 512 pp.

[8] C. E. Murley, “The classification of certain classes of torsion free Abelian groups”, Pasific J. Math., 40:3 (1972), 647–665 | DOI | MR | Zbl

[9] R. A. Bowshell, P. Schultz, “Unital rings whose additive endomorphisms commute”, Math. Ann., 228:3 (1977), 197–214 | DOI | MR | Zbl

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

[11] A. A. Fomin, “A category of matrices representing two categories of Abelian groups”, J. Math. Sci., 154:3 (2008), 430–445 | DOI | MR | Zbl