Skip to main content
SpringerLink
Log in

Functional representation of the orthogonal completion and the divisible envelope of Utumi-torsion-free modules

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. A. Grothendieck and J. Dieudonné, Éléments de Géométrie Algébrique, I, Presses Universitaires de France, Paris (1960).

    Google Scholar 

  2. J. Lambek, “On the representation of modules by sheaves of factor modules,” Can. Math. Bull.,14, No. 3, 359–368 (1971).

    Google Scholar 

  3. V. K. Zakharov, “The orthogonal completion of modules, rings, and Boolean algebras,” in: Ordered Sets and Lattices [in Russian], No. 4, Saratov. Univ. (1976), pp. 54–65.

  4. V. K. Zakharov, “Regular completion of modules,” Mat. Zametki,19, No. 6, 851–859 (1976).

    Google Scholar 

  5. V. K. Zakharov, “Divisible envelope of ℝ-modules,” Usp. Mat. Nauk,31, No. 1, 249–250 (1976).

    Google Scholar 

  6. V. K. Zakharov, “Divisible envelope and orthogonal completion of lattice-ordered modules,” Mat. Sb.,103. No. 3, 346–357 (1977).

    Google Scholar 

  7. N. Bourbaki, Commutative Algebra, Addison-Wesley (1972).

  8. J. Lambek, Torsion Theories, Additive Semantics and Rings of Quotients, Lecture Notes in Math., Vol. 177, Springer-Verlag, Berlin-New York (1971).

    Google Scholar 

  9. A. P. Mishina and L. A. Skornyakov, Abelian Groups and Modules [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  10. J. Lambek, Lectures on Rings and Modules, Blaisdell, Waltham (1966).

    Google Scholar 

  11. R. Grodement, Algebraic Topology and Sheaf Theory [Russian translation], IL, Moscow (1961).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leningrad Textile and Light Industry Institute, USSR

    V. K. Zakharov

Authors
  1. V. K. Zakharov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 27, No. 3, pp. 333–343, March, 1980.

The author thanks the reviewer for his useful remarks.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zakharov, V.K. Functional representation of the orthogonal completion and the divisible envelope of Utumi-torsion-free modules. Mathematical Notes of the Academy of Sciences of the USSR 27, 167–172 (1980). https://doi.org/10.1007/BF01140160

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01140160

Keywords

Search

Navigation