Projective and generating modules over the ring of pseudorational numbers
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 437-448

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The projective, flat, and generating modules over the ring of pseudorational numbers are described. For the projective modules, a complete independent system of invariants is constructed.
Keywords: module over the ring of pseudorational numbers, pseudorational numbers, projective module, generating module, flat module.
A. V. Tsarev. Projective and generating modules over the ring of pseudorational numbers. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 437-448. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a13/
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[1] A. A. Fomin, “Some mixed abelian groups as modules over the ring of pseudo-rational numbers”, Abelian Groups and Modules, Trends in Mathematics, Birkhäuser-Verlag, Basel, 1999, 87–100 | MR | Zbl

[2] P. A. Krylov, E. G. Pakhomova, E. I. Podberezina, “Ob odnom klasse smeshannykh abelevykh grupp”, Vestn. Tomskogo un-ta, 269 (2000), 47–51

[3] A. A. Fomin, “Quotient divisible mixed groups”, Contemp. Math., 273 (2001), 117–128 | MR | Zbl

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

[5] S. V. Cheglyakova, “In'ektivnye moduli nad koltsom psevdoratsionalnykh chisel”, Fundament. i prikl. matem., 7:2 (2001), 627–629 | MR | Zbl

[6] A. V. Tsarev, “Psevdoratsionalnyi rang abelevoi gruppy”, Sib. matem. zh., 46:1 (2005), 217–229 | MR | Zbl

[7] L. Fuks, Beskonechnye abelevy gruppy, t. 1, 2, Mir, M., 1974, 1977 | MR | MR | Zbl

[8] K. Feis, Algebra: koltsa, moduli i kategorii, t. 1, Mir, M., 1977 | MR | Zbl

[9] A. V. Tsarev, “Konechno porozhdennye $R$-moduli”, Nauch. trudy mat. fak-ta MPGU, Prometei, M., 2000, 285–289 | MR

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