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  • Bulletin of the Australian Mathematical Society, Volume 80, Issue 2
  • October 2009, pp. 205-216

SELF-SMALL ABELIAN GROUPS

  • ULRICH ALBRECHT (a1), SIMION BREAZ (a2) and WILLIAM WICKLESS (a3)
  • DOI: http://dx.doi.org/10.1017/S0004972709000185
  • Published online: 01 October 2009
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
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The second author is supported by grant no. PN2CD ID-489.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]U. Albrecht , ‘Mixed Abelian groups with Artinian quasi-endomorphism ring’, Comm. Algebra 25(11) (1997), 34973511.

[2]U. Albrecht , ‘A-projective resolutions and an Azumaya theorem for a class of mixed abelian groups’, Czechoslovak Math. J. 51 (126)(1) (2001), 7393.

[3]U. Albrecht , P. Goeters and W. Wickless , ‘The flat dimension of Abelian groups as E-modules’, Rocky Mountain J. Math. 25(2) (1995), 569590.

[6]D. M. Arnold and C. E. Murley , ‘Abelian groups, A, such that Hom(A,—) preserves direct sums of copies of A’, Pacific J. Math. 56 (1975), 721.

[8]S. Breaz , ‘Self-small Abelian groups as modules over their endomorphism rings’, Comm. Algebra 31 (2003), 49114924.

[9]S. Breaz , ‘Quasi-decompositions for self-small abelian groups’, Comm. Algebra 32 (2004), 13731384.

[10]A. Fomin and W. Wickless , ‘Self-small mixed abelian groups G with G/t(G) finite rank divisible’, Comm. Algebra 26 (1998), 35633580.

[11]A. Fomin and W. Wickless , ‘Quotient divisible abelian groups’, Proc. Amer. Math. Soc. 126 (1998), 4552.

[13]S. Glaz and W. Wickless , ‘Regular and principal projective endomorphism rings of mixed abelian groups’, Comm. Algebra 22 (1994), 11611176.

[15]W. Wickless , ‘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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