Quotient divisible groups and torsion-free groups corresponding to finite Abelian groups

1. Fomin, A. A. 2009, “Invariants for Abelian groups and dual exact sequences”, J. Algebra, vol. 322, no. 7, pp. 2544–2565.

2. Fomin, A. A. 2018, “On the Quotient Divisible Group Theory. II”, J. Math. Sci., vol. 230, no. 3, pp. 457–483.

3. Fomin, A. A. (to appear), “Torsion free abelian groups of finite rank with marked bases”, J. Math. Sci.

4. Yakovlev, А. V. 2010, “Duality of the categories of torsion-free Abelian groups of finite rank and quotient divisible Abelian groups”, J. Math. Sci., vol. 171, no. 3, pp. 416–420.

5. Fomin, A. A.& Wickless, W. J. 1998, “Quotient divisible abelian groups”, Proc. A.M.S., vol. 126, no. 1, pp. 45–52.

6. Fomin, A. A. 2018, “Dual abelian groups of rank 1”, Proceedings of the XV International conference devoted to the 100-th Birthday of Professor N.M. Korobov, May 28–31, 2018, Tula, pp. 62–63. (Russian)

7. Baer, R. 1937, “Abelian groups without elements of finite order”, Duke Math., vol. 3, no. 1, pp. 68–122.

8. Davydova, O. I. 2008, “Rank-1 quotient divisible groups”, J. Math. Sci., vol. 154, no. 3, pp. 295–300.

9. Gordeeva, E. V. & Fomin,A. A.“Completely decomposable homogeneous quotient divisible abelian groups”, Chebyshevskii Sbornik, vol. 19, no. 2, pp. 376–387. (Russian)

10. Fomin, A. A. 2014, “On the Quotient Divisible Group Theory. I”, J. Math. Sci., vol. 197, no. 5, pp. 688–697.

11. Wickless, W. J. 2003, “Direct sums of quotient divisible groups”, Communications in Algebra, vol. 31, no. 1, pp. 79–96.

12. Albrecht, U. & Breaz, S. & Vinsonhaler, C. & Wickless W. 2007, “Cancellation properties for quotient divisible groups”, Journal of Algebra, vol. 317, no. 1, pp. 424–434.

13. Wickless, W. 2006, “Multi-isomorphism for quotient divisible groups”, Houston J. Math., vol. 31, no. 1, pp. 1–19.

14. Files, S. & Wickless, W. 1999, “Direct Sums of Self-Small Mixed Groups”, J. Algebra, vol. 222, no. 1, pp. 1–16.

15. Lyubimtsev, O. V. 2015, “Completely decomposable quotient divisible abelian groups with UA-rings of endomorphisms”, Mathematical Notes, vol. 98, no. 1, pp. 130–137.

16. Lyubimtsev, O. V. 2017, “On determinacy of completely decomposable quotient divisible abelian groups by its endomorphism semigroups”, Russian Math. (Iz. VUZ), vol. 61, no. 10, pp. 65–71.

17. Tsarev, A. V. 2007, “Modules over the ring of pseudorational numbers and quotient divisible groups”, St. Petersburg Math. J., vol. 18, no. 4, pp. 657–669.

18. Tsarev, A. V. 2010, “The module of pseudo-rational relations of a quotient divisible group”, St. Petersburg Math. J., vol. 22, no. 1, pp. 163–174.

19. Tsarev, A. V. 2007, “Pseudorational rank of a quotient divisible group”, J. Math. Sci., vol. 144, no. 2, pp. 4013–4022.

20. Tsarev, A. V. 2013, “T-rings and quotient divisible groups of rank 1”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., vol. 24, no. 4, pp. 50–53.

21. Kryuchkov, N. I. 2018, “Compact Groups That Are Duals of Quotient Divisible Abelian Groups”, J. Math. Sci., vol. 230, no. 3, pp. 428–432.

22. Fomin, A. A. & Wickless, W. 1998, “Self-small mixed abelian groups G with G/T (G) finite rank divisible”, Communications in Algebra, vol. 26, no. 11, pp. 3563–3580.

23. Fomin, A. A. 2008, “Quotient divisible and almost completely decomposable groups”, Models, Modules and Abelian Groups in Memory of A. L. S. Corner, de Gruyter, Berlin – New York, vol. 1, no. 1, pp. 147–167.

24. Fuchs, L. 2015, “Abelian groups”, Switz.: Springer International Publishing.

25. Beaumont, R. A.& Pierce, R. S. 1961, “Torsion free rings”, Ill. J. Math., vol. 5, no. 1, pp. 61–98.

26. Kompantseva, E. I. 2008, “Semisimple rings on completely decomposable Abelian groups”, J. Math. Sci., vol. 154, no. 3, pp. 324–332.

27. Kompantseva, E. I. 2009, “Rings on almost completely decomposable Abelian groups”, J. Math. Sci., vol. 163. no. 6, pp. 688–693.

28. Kompantseva, E. I. 2010, “Torsion-free rings”, J. Math. Sci., vol. 171, no. 2, pp. 213–247.

29. Kompantseva, E. I. & Fomin, A. A. 2015 “Absolute ideals of almost completely decomposable abelian groups”, Chebyshevskii Sb., vol. 16, no. 4, pp. 200–211.

30. Blagoveshchenskaya, Е. А. 2009, “Almost completely decomposable abelian groups and their endomorphism rings”, SPb: Izdelstvo Politehnicheskogo universiteta (Russian).

31. Yakovlev, A. V. 1979, “On the problem of classification of finite rank groups without torsion”, J. Soviet Math., vol. 11, no. 4, pp. 660–663.

32. Thomas, S. 2003, “The Classification Problem for Torsion-Free Abelian Groups of Finite Rank”, JAMS., vol. 16, pp. 233–256.

33. Beaumont, R. & Pierce, R. 1961, “Torsion free groups of rank two”, Mem. Amer. Math. Soc., vol. 38.

34. Fomin, А. А. 1989. “Abelian groups with one τ-adic relation”, Algebra and Logic, vol. 28, no. 1, pp. 57–73.

35. Fomin, А. А. 1984, “Abelian groups with free subgroups of infinite index and their endomorphism groups”, Mathematical Notes, vol. 36, no. 2, pp. 581–585.

36. Fomin, A. A. 1999, “Some mixed abelian groups as modules over the ring of pseudo-rational numbers”, Trends in Math., Burkhauser verlag, Basel/Switzerland, pp. 87–100.