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Endomorphism rings and direct sums of torsion free Abelian groups. (English) Zbl 0329.20033


MSC:

20K15 Torsion-free groups, finite rank
20K25 Direct sums, direct products, etc. for abelian groups
20Kxx Abelian groups
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References:

[1] David M. Arnold, Grothendieck and Whitehead groups of torsion free abelian groups, Bull. Amer. Math. Soc. 79 (1973), 723 – 724. · Zbl 0288.20071
[2] Reinhold Baer, Abelian groups without elements of finite order, Duke Math. J. 3 (1937), no. 1, 68 – 122. · Zbl 0016.20303 · doi:10.1215/S0012-7094-37-00308-9
[3] Hyman Bass, Algebraic \?-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. · Zbl 0174.30302
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[5] Bernard Charles, Sous-groupes fonctoriels et topologies, Studies on Abelian Groups (Symposium, Montpellier, 1967) Springer, Berlin, 1968, pp. 75 – 92 (French).
[6] J. Cook, Thesis, Univ. of Illinois, 1971.
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[8] László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. · Zbl 0209.05503
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[10] Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. · Zbl 0238.16001
[11] E. L. Lady, Summands of finite rank torsion free abelian groups, J. Algebra 32 (1974), 51 – 52. · Zbl 0287.20051 · doi:10.1016/0021-8693(74)90171-9
[12] Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. · Zbl 0365.16001
[13] C. E. Murley, The classification of certain classes of torsion free Abelian groups, Pacific J. Math. 40 (1972), 647 – 655. · Zbl 0261.20045
[14] C. E. Murley, Direct products and sums of torsion-free Abelian groups, Proc. Amer. Math. Soc. 38 (1973), 235 – 241. · Zbl 0275.20095
[15] J. D. Reid, On quasi-decomposition of torsion free Abelian groups, Proc. Amer. Math. Soc. 13 (1962), 550 – 554. · Zbl 0113.25401
[16] R. B. Warfield Jr., Homomorphisms and duality for torsion-free groups, Math. Z. 107 (1968), 189 – 200. · Zbl 0169.03602 · doi:10.1007/BF01110257
[17] H. Zassenhaus, Orders as endomorphism rings of modules of the same rank, J. London Math. Soc. 42 (1967), 180 – 182. · Zbl 0145.26405 · doi:10.1112/jlms/s1-42.1.180
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