Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Nonassociative rings with a single defining relation whose elementary theories are decidable

  • 17 Accesses

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

Literature cited

  1. 1.

    A. I. Zhukov, "Reduced systems of defining relations in nonassociative algebras," Mat. Sb.,27, No. 2, 267–280 (1950).

  2. 2.

    A. I. Shirshov, "Some algorithmic problems for ε-algebras," Sib. Mat. Zh.,3, No. 1, 132–137 (1962).

  3. 3.

    A. I. Shirshov, "Some algorithmic problems for Lie algebras," Sib. Mat. Zh.,3, No. 2, 292–296 (1962).

  4. 4.

    L. A. Bokut', "Unsolvability of the problem of equality and subalgebras of finitely defined Lie algebras," Izv. Akad. Nauk SSSR, Ser. Mat.,36, No. 6, 1173–1219 (1972).

  5. 5.

    Yu. M. Vazhenin, "Algorithmic problems and hierarchies of first-order languages," Algebra Logika,26, No. 4, 419–434 (1987).

  6. 6.

    Yu. M. Vazhenin, "Semigroups with a single defining relation whose elementary theories are decidable," Sib. Mat. Zh.,24, No. 1, 40–49 (1983).

  7. 7.

    K. A. Zhevlakov, A. I. Slin'ko, I. P. Shestakov, and A. I. Shirshov, Near-Associative Rings [in Russian], Nauka, Moscow (1978).

  8. 8.

    Yu. L. Ershov, I. A. Lavrov, A. D. Taimanov, and M. A. Taitslin, "Elementary theories," Usp. Mat. Nauk,20, No. 5, 37–108 (1965).

  9. 9.

    Yu. L. Ershov and E. A. Palyutin, Mathematical Logic [in Russian], Nauka, Moscow (1987).

  10. 10.

    J. Barwise (ed.), Handbook of Mathematical Logic, North Holland, Amsterdam (1977).

  11. 11.

    Yu. M. Vazhenin, "Critical theories," Sib. Mat. Zh.,29, No. 1, 23–31 (1988).

Download references

Additional information

Translated from Algebra i Logika, Vol. 29, No. 5, pp. 509–522, September–October, 1990.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vazhenin, Y.M. Nonassociative rings with a single defining relation whose elementary theories are decidable. Algebr Logic 29, 339–348 (1990). https://doi.org/10.1007/BF02215282

Download citation

Keywords

  • Mathematical Logic
  • Elementary Theory
  • Nonassociative Ring