Literature Cited
L. Ya. Kulikov, “Generalized primary groups,” Tr. Mosk. Mat. Obshch.,1, 247–326 (1952).
A. A. Beaumont and R. S. Pierce, “Torsion-free rings,” Illinois J. Math.,5, No. 1, 61–98 (1961).
R. Baer, “Abelian groups without elements of finite order,” Duke Math. J.,3, No. 1, 68–122 (1937).
D. M. Arnold, “A duality for torsion-free modules of finite rank over a discrete valuation ring,” Proc. London Math. Soc.,24, No. 3, 204–216 (1972).
D. M. Arnold, “A duality for quotient divisible Abelian groups of finite rank,” Pac. J. Math.,42, No. 1, 11–15 (1972).
R. B. Warfield, “Homomorphisms and duality for torsion-free groups,” Math. Z.,107, No. 1, 189–200 (1968).
L. Fuchs, Infinite Abelian Groups, Vol. 1, Academic Press, New York-London (1970).
F. Richman, “A class of rank 2 torsion-free groups,” in: Studies on Abelian Groups, Paris (1968), pp. 327–333.
C. E. Murley, “The classification of certain classes of torsion-free Abelian groups,” Pac. J. Math.,40, No. 3, 647–665 (1972).
L. Ya. Kulikov, Algebra and Number Theory [in Russian], Vysshaya Shkola, Moscow (1979).
M. Bourbaki, Algebra I, Hermann, Paris (1974), Chaps. I–III.
A. A. Fomin, “Tensor products of torsion-free Abelian groups,” Sib. Mat. Zh.,16, No. 5, 1071–1080 (1975).
A. A. Fomin, “Monogeneous ε-groups,” in: Proceedings 7th All-Union Symposium on Group Theory, Krasnoyarsk State Univ., 128 (1980).
D. W. Dubois, “Cohesive groups and p-adic integers,” Publ. Math. Debrecen,12, No. 1, 51–58 (1965).
A. A. Fomin, “Abelian groups with free subgroups of infinite index and their endomorphism rings,” mat. Zametki,36, No. 2, 179–187 (1984).
A. A. Fomin, “Abelian groups with free pure subgroups,” in: Proceedings 9th All-Union Symposium on Group Theory, MGPI im. V. I. Lenina, Moscow (1984), p. 162.
Additional information
Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 27, No. 4, pp. 117–127, July–August, 1986.
Rights and permissions
About this article
Cite this article
Fomin, A.A. Duality in some classes of torsion-free Abelian groups of finite rank. Sib Math J 27, 563–571 (1986). https://doi.org/10.1007/BF00969169
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969169