Skip to main content

Abelian dqt-Groups and Rings on Them

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.


The absolute radical of an Abelian group G is the intersection of radicals of all associative rings with additive group G. The problem of describing absolute radicals was formulated by L. Fuchs. He described the absolute Jacobson radical of a torsion Abelian group. In this work, the absolute Jacobson radical and the absolute nil-radical are investigated in some mixed Abelian group classes.

This is a preview of subscription content, access via your institution.


  1. 1.

    C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York (1962).

    MATH  Google Scholar 

  2. 2.

    L. Fuchs, Infinite Abelian Groups, Vols. 1, 2, Academic Press, New York (1970, 1973).

  3. 3.

    L. Fuchs and K. M. Rangaswamy, “On generalized regular rings,” Math. Z., 107, 71–81 (1968).

    Article  MATH  MathSciNet  Google Scholar 

  4. 4.

    A. V. Ivanov, “Abelian groups with self-injective rings of endomorphisms and with rings of endomorphisms with the annihilator condition,” in Abelian Groups and Modules [in Russian], TSU, Tomsk (1982), pp. 93–109.

  5. 5.

    N. Jacobson, Structure of Rings, Colloq. Publ., Vol. 37, Amer. Math. Soc. (1956).

  6. 6.

    E. I. Kompantseva, “Torsion-free rings,” J. Math. Sci., 171, No. 2, 213–247 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  7. 7.

    E. I. Kompantseva, “Absolute nil-ideals of Abelian groups,” Fundam. Prikl. Mat., 17, No. 8, 63–76 (2011/2012).

  8. 8.

    P. A. Krylov, “Mixed Abelian groups as modules over their endomorphism rings,” Fundam. Prikl. Mat., 6, No. 3, 793–812 (2000).

    MATH  MathSciNet  Google Scholar 

  9. 9.

    K. M. Rangaswamy, “Abelian groups with endomorphic images of special types,” J. Algebra, 6, 271–280 (1967).

    Article  MATH  MathSciNet  Google Scholar 

  10. 10.

    E. H. Toubassi and D. A. Lawver, “Height-slope and splitting length of Abelian groups,” Publ. Mat., 20, 63–71 (1973).

    MATH  MathSciNet  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to E. I. Kompantseva.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 53–67, 2013.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kompantseva, E.I. Abelian dqt-Groups and Rings on Them. J Math Sci 206, 494–504 (2015).

Download citation


  • Abelian Group
  • Associative Ring
  • Invariant Subgroup
  • Pure Subgroup
  • Basic Subgroup