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Modules over the ring of pseudorational numbers and quotient divisible groups


Author: A. V. Tsarev
Translated by: A. V. Yakovlev
Original publication: Algebra i Analiz, tom 18 (2006), nomer 4.
Journal: St. Petersburg Math. J. 18 (2007), 657-669
MSC (2000): Primary 16L99
DOI: https://doi.org/10.1090/S1061-0022-07-00965-X
Published electronically: May 29, 2007
MathSciNet review: 2262588
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Abstract | References | Similar Articles | Additional Information

Abstract: Structure theorems are obtained for some classes of modules over the ring of pseudorational numbers and some classes of quotient divisible mixed groups.


References [Enhancements On Off] (What's this?)

  • 1. L. Fuchs, Infinite abelian groups. Vols. I, II, Pure Appl. Math., vols. 36, 36-II, Acad. Press, New York-London, 1970, 1973. MR 0255673 (41:333); MR 0349869 (50:2362)
  • 2. A. A. Fomin, Some mixed abelian groups as modules over the ring of pseudo-rational numbers, Abelian Groups and Modules (Dublin, 1988), Trends Math., Birkhäuser Verlag, Basel, 1999, pp. 87-100. MR 1735560 (2001b:20096)
  • 3. A. A. Fomin and W. Wickless, Quotient divisible abelian groups, Proc. Amer. Math. Soc. 126 (1998), 45-52. MR 1443826 (98c:20100)
  • 4. A. A. Fomin, Quotient divisible mixed groups, Abelian Groups, Rings and Modules (Perth, 2000), Contemp. Math., vol. 273, Amer. Math. Soc., Providence, RI, 2001, pp. 117-128. MR 1817156 (2002b:20079)
  • 5. L. Fuchs and K. M. Rangaswamy, On generalized regular rings, Math. Z. 107 (1968), 71-81. MR 0233850 (38:2171)
  • 6. S. Glaz and W. Wickless, Regular and principal projective endomorphism rings of mixed abelian groups, Comm. Algebra 22 (1994), 1161-1176. MR 1261253 (95a:20060)
  • 7. W. Wickless, A functor from mixed groups to torsion-free groups, Abelian Group Theory and Related Topics (Oberwolfach, 1993), Contemp. Math., vol. 171, Amer. Math. Soc., Providence, RI, 1994, pp. 407-417. MR 1293158 (95k:20090)
  • 8. U. E. Albrecht, Mixed abelian groups with Artinian quasi-endomorphism ring, Comm. Algebra 25 (1997), 3497-3511. MR 1468818 (98j:20081)
  • 9. A. A. Fomin and W. Wickless, Self-small mixed abelian groups $ G$ with $ G/T(G)$ finite rank divisible, Comm. Algebra 26 (1998), 3563-3580. MR 1647118 (99j:20061)
  • 10. -, Categories of mixed and torsion-free finite rank abelian groups, Abelian Groups and Modules (Padova, 1994), Math. Appl., vol. 343, Kluwer Acad. Publ., Dordrecht, 1995, pp. 185-192. MR 1378197 (97c:20083)
  • 11. A. V. Yakovlev and N'Famara Kamara, Mixed abelian groups of finite rank and their direct decompositions, Vestnik S.-Peterburg. Univ. Mat. Mekh. Astronom. 1993, vyp. 2, 57-61; English transl., Vestnik St. Petersburg Univ. Math. 26 (1993), no. 2, 50-53. MR 1370233 (96k:20112)
  • 12. P. A. Krylov, Mixed abelian groups as modules over their endomorphism rings, Fundam. Prikl. Mat. 6 (2000), no. 3, 793-812. (Russian) MR 1801329 (2001m:20099)
  • 13. P. A. Krylov, E. G. Pakhomova, and E. I. Podberezina, On a class of mixed abelian groups, Vestnik Tomsk. Univ. 269 (2000). (Russian).
  • 14. S. V. Cheglyakova, Injective modules over the ring of pseudorational numbers, Fundam. Prikl. Mat. 7 (2001), no. 2, 627-629. (Russian) MR 1866471 (2002h:16007)
  • 15. D. M. Arnold, Finite rank abelian torsion free abelian groups and rings, Lecture Notes in Math., vol. 931, Springer-Verlag, Berlin-New York, 1982. MR 665251 (84d:20002)
  • 16. A. V. Tsarev, The pseudorational rank of an abelian group, Sibirsk. Mat. Zh. 46 (2005), no. 1, 217-229; English transl., Siberian Math. J. 46 (2005), no. 1, 172-181. MR 2141315 (2006a:20099)

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Additional Information

A. V. Tsarev
Affiliation: Moscow State Pedagogical University, Moscow, Russia
Email: an-tsarev@yandex.ru

DOI: https://doi.org/10.1090/S1061-0022-07-00965-X
Keywords: Abelian groups, quotient divisible groups, ring of pseudorational numbers, pseudorational rank, module of pseudorational relations
Received by editor(s): November 21, 2005
Published electronically: May 29, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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