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Algorithmic problems in associative algebras

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References

  1. A. I. Shirshov, “Subalgebras of free Lie algebras,”Mat. Sb.,33, No. 2, 441–452 (1953).

    Google Scholar 

  2. P. M. Cohn, “Subalgebras of free associative algebras,”Proc. London Math. Soc.,14, No. 56, 618–632 (1964).

    Google Scholar 

  3. U. U. Umirbaev, “On approximation of free Lie algebras with respect to occurrence,” in:Monoids, Rings, and Algebras, Proc. Tartu Univ. [in Russian],878 (1990), pp. 147–152.

    Google Scholar 

  4. A. A. Mikhalyov, “Right ideals in a free associative algebra generated by free colored Lie (p-)superalgebras,” to appear in:Usp. Mat. Nauk.

  5. G. A. Noskov, “Occurrence problem for a polynomial ring,”Sib. Mat. Zh.,19, No. 6, 1413–1414 (1976).

    Google Scholar 

  6. D. Shannon and M. Sweedler, “Using Grobner bases to determine algebra membership, split surjective algebra homomorphisms, determine birational equivalence,”J. Symb. Comp.,6, No. 2–3, 267–273 (1988).

    Google Scholar 

  7. A. I. Shirshov, “Some algorithmic problems forε-algebras,”Sib. Mat. Zh.,3, No. 1, 132–137 (1962).

    Google Scholar 

  8. U. U. Umirbaev, “Occurrence problem for free associative algebras,” in:11th Inter-Republican Conference on Mathematical Logic, Abstracts [in Russian], Kazan' (1992), p. 145.

  9. G. P. Kukin, “Word problem and free products of Lie algebras and associative rings,”Sib. Mat. Zh.,24, No. 2, 86–95 (1983).

    Google Scholar 

  10. I. L. Mel'nichuk, M. V. Sapir, and O. G. Kharlampovich, “Word problem in varieties of semigroups, rings, and Lie algebras,”Sib. Mat. Zh.,27, No. 6, 144–156 (1986).

    Google Scholar 

  11. Dnestrov Notebook [in Russian], Novosibirsk (1982).

  12. R. C. Lyndon and P. E. Schupp,Combinatorial Group Theory, Springer, Berlin (1977).

    Google Scholar 

  13. A. I. Mal'tsev,Algorithms and Recursive Functions, 2nd edn. [in Russian], Mir, Moscow (1986).

    Google Scholar 

  14. M. V. Sapir and O. G. Kharlampovich, “World problem in varieties of associative algebras and Lie algebras,”Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 6, 76–84 (1989).

    Google Scholar 

  15. G. M. Bergman and W. Dicks, “On universal derivations,”J. Algebra,36, 194–211 (1975).

    Article  Google Scholar 

  16. G. Hochschild, “On the cohomology groups of an associative algebra,”Ann. Math.,2, No. 46, 58–67 (1945).

    Google Scholar 

  17. L. A. Bokut',Associative Rings, I [in Russian], Novosibirsk University, Novosibirsk (1977).

    Google Scholar 

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Translated fromAlgebra i Logika, Vol. 32, No. 4, pp. 450–470, July–August, 1993.

Translated by O. Bessonova

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Umirbaev, U.U. Algorithmic problems in associative algebras. Algebr Logic 32, 244–255 (1993). https://doi.org/10.1007/BF02261749

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  • DOI: https://doi.org/10.1007/BF02261749

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