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Axiomatizability of radical and semisimple classes of modules and Abelian groups

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Literature cited

  1. 1.

    P. C. Eklof and G. Sabbagh, “Model completions and modules,” Ann. Math. Logic,2, No. 3, 251–295 (1971).

  2. 2.

    P. C. Eklof and G. Sabbagh, “Definiability properties for modules and rings,” J. Symb. Logic,36, 629–649 (1971).

  3. 3.

    G. Sabbagh, “Aspects logiques de la purete dans les modules,” C. R. Acad. Sci. A,271, 909–912 (1969).

  4. 4.

    N. Ya. Komarnitskii, “Torsions and quasivarieties of modules,” in: Questions of the Qualitative Theory of Differential Equations and Their Applications [in Russian], Kiev (1978), pp. 19–21.

  5. 5.

    M. Y. Prest, “Some model-theoretic aspects of torsion theories,” J. Pure Appl. Algebra,12, No. 3, 295–310 (1978).

  6. 6.

    N. Ya. Komarnitskii, “On the axiomatizability of some classes of modules connected with torsions,” in: Algebras and Modules [in Russian], Kishinev (1980), pp. 35–48.

  7. 7.

    C. U. Jensen and P. Vamos, “On the axiomatizability of certain classes of modules,” Math. Z., 167, No. 3, 227–237 (1979).

  8. 8.

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

  9. 9.

    B. Stenström, Rings and Modules of Quotients, Springer-Verlag, Berlin-New York (1975).

  10. 10.

    A. I. Mal'tsev, Algebraic Systems, Springer-Verlag, Berlin-Heidelberg-New York (1973).

  11. 11.

    C. C. Chang and H. J. Keisler, Model Theory, North-Holland/Elsevier, Amsterdam-London-New York (1973).

  12. 12.

    W. Szmielew, “Elementary properties of Abelian groups,” Fund. Math.,41, 203–271 (1955).

  13. 13.

    E. L. Gorbachuk and N. Ya. Komarnitskii, “I-radicals and their properties,” Ukr. Mat. Zh.,30, No. 2, 212–217 (1978).

  14. 14.

    V. Dlab, “A characterization of perfect rings,” Pac. J. Math.,33, No. 1, 79–88 (1970).

  15. 15.

    N. Ya. Komarnitskii, “Duo-rings over which all torsions are S-torsions,” Mat. Issled.,48, 65–68 (1978).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 34, No. 2, pp. 151–157, March–April, 1982.

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Gorbachuk, E.L., Komarnitskii, N.Y. Axiomatizability of radical and semisimple classes of modules and Abelian groups. Ukr Math J 34, 124–129 (1982). https://doi.org/10.1007/BF01091514

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Keywords

  • Abelian Group
  • Semisimple Class