Siberian Mathematical Journal

, Volume 60, Issue 1, pp 62–70 | Cite as

Separable Enumerations of Division Rings and Effective Embeddability of Rings Therein

  • N. Kh. KasymovEmail author
  • F. N. IbragimovEmail author


We prove the negativity of separable enumerations of division rings and establish that the effective embeddability of a commutative integral domain in a separably enumerated field is equivalent to its negativity.


enumerated algebras and morphisms topological enumerated algebra separable enumerations of division rings locally positive and negatives groups effective embeddability of rings into fields 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Soare R. I., Recursively Enumerable Sets and Degrees, Springer–Verlag, Heidelberg (1987).CrossRefzbMATHGoogle Scholar
  2. 2.
    Ershov Yu. L., The Theory of Enumerations [Russian], Nauka, Moscow (1977).Google Scholar
  3. 3.
    Ershov Yu. L., Decidability Problems and Constructive Models [Russian], Nauka, Moscow (1980).Google Scholar
  4. 4.
    Ershov Yu. L. and Goncharov S. S., Constructive Models, Ser. Siberian School of Algebra and Logic, Kluwer Academic/Plenum Publishers, New York, etc. (2000).Google Scholar
  5. 5.
    Khoussainov B., Slaman T., and Semukhin P., “\(\Pi_1^0\)–Presentations of algebras,” Arch. Math. Logic, vol. 45, No. 6, 769–781 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kasymov N. Kh., “Homomorphisms onto effectively separable algebras,” Sib. Math. J., vol. 57, No. 1, 36–50 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kasymov N. Kh., “Recursively separable enumerated algebras,” Russian Math. Surveys, vol. 51, No. 3, 509–538 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Malcev A. I., “To the general theory of algebraic systems,” Mat. Sb., vol. 35, No. 1, 3–20 (1954).MathSciNetGoogle Scholar
  9. 9.
    Malcev A., “On the immersion of an algebraic ring into a field,” Math. Ann., vol. 113, 686–691 (1937).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Mirzo Ulugbek National University of UzbekistanTashkentUzbekistan

Personalised recommendations