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SELF-SMALL ABELIAN GROUPS

  • ULRICH ALBRECHT (a1), SIMION BREAZ (a2) and WILLIAM WICKLESS (a3)
Abstract
Abstract

This paper investigates self-small abelian groups of finite torsion-free rank. We obtain a new characterization of infinite self-small groups. In addition, self-small groups of torsion-free rank 1 and their finite direct sums are discussed.

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Copyright
Corresponding author
For correspondence; e-mail: albreuf@mail.auburn.edu
Footnotes
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The second author is supported by grant no. PN2CD ID-489.

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References
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[1] Albrecht U., ‘Mixed Abelian groups with Artinian quasi-endomorphism ring’, Comm. Algebra 25(11) (1997), 34973511.
[2] Albrecht U., ‘A-projective resolutions and an Azumaya theorem for a class of mixed abelian groups’, Czechoslovak Math. J. 51 (126)(1) (2001), 7393.
[3] Albrecht U., Goeters P. and Wickless W., ‘The flat dimension of Abelian groups as E-modules’, Rocky Mountain J. Math. 25(2) (1995), 569590.
[4] Albrecht U. and Wickless W., Finitely Generated and Cogenerated QD-groups, Rings, Modules, Algebras, and Abelian Groups, Lecture Notes in Pure and Appl. Math, 236  (Dekker, New York, 2004), pp. 1326.
[5] Arnold D. M., Finite Rank Torsion Free Abelian Groups and Rings, Lecture Notes in Mathematics, 931  (Springer-Verlag, Berlin, 1982).
[6] Arnold D. M. and Murley C. E., ‘Abelian groups, A, such that Hom(A,—) preserves direct sums of copies of A’, Pacific J. Math. 56 (1975), 721.
[7] Beaumont R. A. and Pierce R. S., ‘Torsion-free rings’, Illinois J. Math. 5 (1961), 6198.
[8] Breaz S., ‘Self-small Abelian groups as modules over their endomorphism rings’, Comm. Algebra 31 (2003), 49114924.
[9] Breaz S., ‘Quasi-decompositions for self-small abelian groups’, Comm. Algebra 32 (2004), 13731384.
[10] Fomin A. and Wickless W., ‘Self-small mixed abelian groups G with G/t(G) finite rank divisible’, Comm. Algebra 26 (1998), 35633580.
[11] Fomin A. and Wickless W., ‘Quotient divisible abelian groups’, Proc. Amer. Math. Soc. 126 (1998), 4552.
[12] Fuchs L., Infinite Abelian Groups Vols. I and II (Academic Press, New York, 1970/1973).
[13] Glaz S. and Wickless W., ‘Regular and principal projective endomorphism rings of mixed abelian groups’, Comm. Algebra 22 (1994), 11611176.
[14] Walker E., ‘Quotient categories and quasi-isomorphisms of abelian groups’, in: Proc. Colloq. Abelian Groups (Akademiai Kiado, Budapest, 1963), pp. 147162.
[15] Wickless W., ‘A funtor from mixed groups to torsion free groups’, Contemp. Math. 171 (1995), 407419.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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