Modules over the ring of pseudorational numbers and quotient divisible groups
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A. V. Tsarev
Translated by: A. V. Yakovlev - St. Petersburg Math. J. 18 (2007), 657-669
- DOI: https://doi.org/10.1090/S1061-0022-07-00965-X
- Published electronically: May 29, 2007
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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
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- Alexander A. Fomin, Some mixed abelian groups as modules over the ring of pseudo-rational numbers, Abelian groups and modules (Dublin, 1998) Trends Math., Birkhäuser, Basel, 1999, pp. 87–100. MR 1735560
- A. Fomin and W. Wickless, Quotient divisible abelian groups, Proc. Amer. Math. Soc. 126 (1998), no. 1, 45–52. MR 1443826, DOI 10.1090/S0002-9939-98-04230-0
- Alexander 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, DOI 10.1090/conm/273/04428
- László Fuchs and K. M. Rangaswamy, On generalized regular rings, Math. Z. 107 (1968), 71–81. MR 233850, DOI 10.1007/BF01111051
- S. Glaz and W. Wickless, Regular and principal projective endomorphism rings of mixed abelian groups, Comm. Algebra 22 (1994), no. 4, 1161–1176. MR 1261253, DOI 10.1080/00927879408824899
- W. J. 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, DOI 10.1090/conm/171/01792
- Ulrich Albrecht, Mixed abelian groups with Artinian quasi-endomorphism ring, Comm. Algebra 25 (1997), no. 11, 3497–3511. MR 1468818, DOI 10.1080/00927879708826065
- A. Fomin and W. Wickless, Self-small mixed abelian groups $G$ with $G/T(G)$ finite rank divisible, Comm. Algebra 26 (1998), no. 11, 3563–3580. MR 1647118, DOI 10.1080/00927879808826360
- Alexander A. Fomin and William J. Wickless, 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
- A. V. Yakovlev and N’Famara Kamara, Mixed abelian groups of finite rank and their direct decompositions, Vestnik S.-Peterburg. Univ. Mat. Mekh. Astronom. vyp. 2 (1993), 57–61, 125 (Russian, with English and Russian summaries); English transl., Vestnik St. Petersburg Univ. Math. 26 (1993), no. 2, 50–53. MR 1370233
- P. A. Krylov, Mixed abelian groups as modules over their endomorphism rings, Fundam. Prikl. Mat. 6 (2000), no. 3, 793–812 (Russian, with English and Russian summaries). MR 1801329
- P. A. Krylov, E. G. Pakhomova, and E. I. Podberezina, On a class of mixed abelian groups, Vestnik Tomsk. Univ. 269 (2000). (Russian).
- S. V. Cheglyakova, Injective modules over the ring of pseudorational numbers, Fundam. Prikl. Mat. 7 (2001), no. 2, 627–629 (Russian, with English and Russian summaries). MR 1866471
- David M. Arnold, Finite rank torsion free abelian groups and rings, Lecture Notes in Mathematics, vol. 931, Springer-Verlag, Berlin-New York, 1982. MR 665251
- A. V. Tsarev, The pseudorational rank of an abelian group, Sibirsk. Mat. Zh. 46 (2005), no. 1, 217–229 (Russian, with Russian summary); English transl., Siberian Math. J. 46 (2005), no. 1, 172–181. MR 2141315, DOI 10.1007/s11202-005-0018-x
Bibliographic Information
- A. V. Tsarev
- Affiliation: Moscow State Pedagogical University, Moscow, Russia
- Email: an-tsarev@yandex.ru
- Received by editor(s): November 21, 2005
- Published electronically: May 29, 2007
- © Copyright 2007 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 657-669
- MSC (2000): Primary 16L99
- DOI: https://doi.org/10.1090/S1061-0022-07-00965-X
- MathSciNet review: 2262588