Ukrainian Mathematical Journal

, Volume 67, Issue 9, pp 1386–1399 | Cite as

Relative Extensions of Modules and Homology Groups

  • L. Mao
  • H. Zhu
Article

We introduce the concepts of relative (co)extensions of modules and explore the relationship between the relative (co)extensions of modules and relative (co)homology groups. Some applications are given.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. L. Chen and N. Q. Ding, “A note on existence of envelopes and covers,” Bull. Austral. Math. Soc., 54, 383–390 (1996).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    F. Couchot, “RD-flatness and RD-injectivity,” Comm. Algebra, 34, 3675–3689 (2006).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    E. E. Enochs, “Injective and flat covers, envelopes and resolvents,” Isr. J. Math., 39, 189–209 (1981).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    E. E. Enochs, “Flat covers and flat cotorsion modules,” Proc. Amer. Math. Soc., 92, No. 2, 179–184 (1984).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter, Berlin; New York (2000).CrossRefMATHGoogle Scholar
  6. 6.
    L. Fuchs and L. Salce, “Modules over non-Noetherian domains,” Math. Surv. Monogr., Amer. Math. Soc., Providence, Vol. 84 (2001).Google Scholar
  7. 7.
    J. R. García Rozas and B. Torrecillas, “Relative injective covers,” Comm. Algebra, 22, 2925–2940 (1994).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    R. Göbel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, de Gruyter, Berlin–New York (2006).CrossRefMATHGoogle Scholar
  9. 9.
    P. A. Guil Asensio and I. Herzog, “Sigma-cotorsion rings,” Adv. Math., 191, 11–28 (2005).MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    S. Maclane, Homology, Springer, Berlin, etc. (1963).Google Scholar
  11. 11.
    L. X. Mao, “Properties of RD-projective and RD-injective modules,” Turk. J. Math., 35, No. 2, 187–205 (2011).MathSciNetMATHGoogle Scholar
  12. 12.
    J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York (1979).MATHGoogle Scholar
  13. 13.
    R. B. Warfield (Jr.), “Purity and algebraic compactness for modules,” Pacif. J. Math., 28, 699–719 (1969).Google Scholar
  14. 14.
    J. Xu, “Flat covers of modules,” Lect. Notes Math., Springer, Berlin etc., 1634 (1996).Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • L. Mao
    • 1
  • H. Zhu
    • 2
  1. 1.Nanjing Institute of TechnologyNanjingChina
  2. 2.Zhejiang University of TechnologyHangzhouChina

Personalised recommendations