Ukrainian Mathematical Journal

, Volume 64, Issue 6, pp 875–880 | Cite as

On properties of n-totally projective Abelian p-groups

  • P. Keef
  • P. Danchev
Article
First Online:
Received:

We prove some properties of n-totally projective Abelian p-groups. Under certain additional conditions for the group structure, we obtain an equivalence between the notions of n-total projectivity and strong n-total projectivity. We also show that n-totally projective A-groups are isomorphic if they have isometric p n -socles

Keywords

Direct Summand Projective Group Countable Group Projective Resolution Separable Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Danchev and P. Keef, “An application of set theory to ω + n-totally p ω+n-projective primary Abelian groups,” Mediterr. J. Math., 8, No. 4, 525–542 (2011).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    L. Fuchs, Infinite Abelian Groups, Academic Press, New York–London (1970, 1973), Vol. 1, 2.MATHGoogle Scholar
  3. 3.
    P. Griffith, Infinite Abelian Group Theory, Univ. Chicago Press, Chicago–London (1970).MATHGoogle Scholar
  4. 4.
    P. Hill, “On the structure of Abelian p-groups,” Trans. Amer. Math. Soc., 288, No. 2, 505–525 (1985).MathSciNetMATHGoogle Scholar
  5. 5.
    P. Hill and C. Megibben, “On direct sums of countable groups and generalizations,” Stud. Abelian Groups, 183–206 (1968).Google Scholar
  6. 6.
    P. Keef, “On ω1-p ω+n-projective primary Abelian groups,” J. Algebra Numb. Th. Acad., 1, No. 1, 41–75 (2010).MATHGoogle Scholar
  7. 7.
    P. Keef and P. Danchev, “On n-simply presented primary Abelian groups,” Houston J. Math., 38, No. 3 (2012).Google Scholar
  8. 8.
    P. Keef and P. Danchev, “On m, n-balanced projective and m, n-totally projective primary Abelian groups” (to appear).Google Scholar
  9. 9.
    R. Nunke, “On the structure of tor II,” Pacif. J. Math., 22, 453–464 (1967).MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • P. Keef
    • 1
  • P. Danchev
    • 2
  1. 1.Whitman CollegeWalla WallaUSA
  2. 2.“P. Hilendarski” Plovdiv UniversityPlovdivBulgaria

Personalised recommendations