Geodesic
Base fields of $\mathrm{csp}$-rings
Algebra i logika, Tome 49 (2010) no. 4, pp. 555-565.

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

We study into the question of which fields may serve as base fields for $\mathrm{csp}$-rings. It is proved that every algebraic extension of a field $\mathbf Q$ is the base field of some $\mathrm{csp}$-ring. Also it shown that in studying base fields, we may confine ourselves to treating only $\mathrm{csp}$-rings of idempotent cocharacteristic, or only regular $\mathrm{csp}$-rings.
Keywords: $\mathrm{csp}$-ring, base field. 
@article{AL_2010_49_4_a5,
     author = {E. A. Timoshenko},
     title = {Base fields of $\mathrm{csp}$-rings},
     journal = {Algebra i logika},
     pages = {555--565},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_4_a5/}
}
TY  - JOUR
AU  - E. A. Timoshenko
TI  - Base fields of $\mathrm{csp}$-rings
JO  - Algebra i logika
PY  - 2010
SP  - 555
EP  - 565
VL  - 49
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2010_49_4_a5/
LA  - ru
ID  - AL_2010_49_4_a5
ER  - 
%0 Journal Article
%A E. A. Timoshenko
%T Base fields of $\mathrm{csp}$-rings
%J Algebra i logika
%D 2010
%P 555-565
%V 49
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2010_49_4_a5/
%G ru
%F AL_2010_49_4_a5
E. A. Timoshenko. Base fields of $\mathrm{csp}$-rings. Algebra i logika, Tome 49 (2010) no. 4, pp. 555-565. http://geodesic.mathdoc.fr/item/AL_2010_49_4_a5/

[1] A. A. Fomin, “Some mixed abelian groups as modules over the ring of pseudo-rational numbers”, Abelian groups and modules, Proc. int. conf. (Dublin, Ireland, August 10–14, 1998), Trends Math., eds. P. C. Eklof et al., Birkhäuser, Basel, 1999, 87–100 | MR | Zbl

[2] P. A. Krylov, “Smeshannye abelevy gruppy kak moduli nad svoimi koltsami endomorfizmov”, Fundam. prikl. matem., 6:3 (2000), 793–812 | MR | Zbl

[3] P. A. Krylov, “Nasledstvennye koltsa endomorfizmov smeshannykh abelevykh grupp”, Sib. matem. zh., 43:1 (2002), 108–119 | MR | Zbl

[4] L. Fuchs, I. Halperin, “On the imbedding of a regular ring in a regular ring with identity”, Fundam. Math., 54 (1964), 285–290 | Zbl

[5] L. Fuchs, K. M. Rangaswamy, “On generalized regular rings”, Math. Z., 107:1 (1968), 71–81 | DOI | MR | Zbl

[6] A. V. Tsarëv, “Moduli nad koltsom psevdoratsionalnykh chisel i faktornodelimye gruppy”, Algebra i analiz, 18:4 (2006), 198–214 | MR | Zbl

[7] A. V. Tsarëv, “Proektivnye i obrazuyuschie moduli nad koltsom psevdoratsionalnykh chisel”, Matem. zametki, 80:3 (2006), 437–448 | MR | Zbl

[8] E. G. Zinovev, “csp-koltsa kak obobschenie kolets psevdoratsionalnykh chisel”, Fundam. prikl. matem., 13:3 (2007), 35–38 | MR | Zbl

[9] E. G. Zinovev, “In'ektivnye i delimye moduli nad csp-koltsami”, Vestnik TGU, 299, 2007, 96–97

[10] E. G. Zinovev, “Konechno porozhdënnye moduli nad koltsami psevdoalgebraicheskikh chisel”, Cb. Mezhd. algebr. konf., posvyasch. 100-letiyu so dnya rozhdeniya A. G. Kurosha, Tezisy dokladov, MMF MGU, M., 2008, 104–105

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

[12] S. B. Katok, $p$-adicheskii analiz v sravnenii s veschestvennym, MTsNMO, M., 2004

[13] M. C. R. Butler, “On locally free torsion-free rings of finite rank”, J. London Math. Soc., 43:1 (1968), 297–300 | DOI | MR | Zbl