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On decidability of theories of finitely generated quasigroups in R-varieties of groups

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Literature Cited

  1. T. Evans, “The word problem for abstract algebras,” J. London Math.,26, 64–67 (1951).

    Google Scholar 

  2. T. Evans, “On multiplicative systems defined by generators and relations. I. Normal form theorems,” Proc. Cambridge Phil. Soc.,47, 637–645 (1951).

    Google Scholar 

  3. T. Evans, “The isomorphism problem for some classes of multiplicative systems,” Trans. Am. Soc.,109, No. 2, 303–312 (1963).

    Google Scholar 

  4. A. A. Gvaramiya and M. M. Glukhov, “On algorithmic problems for certain classes of quasigroups,” Dokl. Akad. Nauk SSSR,177, No. 1, 14–16 (1967).

    Google Scholar 

  5. A. A. Gvaramiya and M. M. Glukhov, “Solution of basic algorithmic problems in certain classes of quasigroups with identities,” Sib. Mat. Zh.,10, No. 2, 297–317 (1969).

    Google Scholar 

  6. M. M. Glukhov, “On free products and algorithmic problems in R-varieties of universal algebras,” Dokl. Akad. Nauk SSSR,193, No. 3, 514–517 (1970).

    Google Scholar 

  7. M. M. Glukhov and A. I. Mukhin, “On equations over quasigroups,” Sib. Mat. Zh.,18, No. 4, 755–764 (1977).

    Google Scholar 

  8. L. V. Shabunin, “On the decidability of theories of certain nonassociative finitely generated algebras” Devyat. Vsesoyuz. Konf. Mat. Log., Tez. Dokl., Leningrad (1988).

  9. A. I. Mal'tsev, “Axiomatizable classes of locally free algebras of certain types,” Sib. Mat. Zh.,3, No. 5, 729–743 (1962).

    Google Scholar 

  10. M. M. Glukhov, “R-varieties of quasigroups and lenses,” Problems in the Theory of Quasigroups and Lenses, 37–47, Kishinev (1970).

  11. M. M. Glukhov, “Free expansions and algorithmic problems in R-varieties of universal algebras,” Mat. Sb.,85, No. 3, 307–338 (1971).

    Google Scholar 

  12. E. A. Khalezov, “Automorphisms of primitive quasigroups,” Mat. Sb.,53, No. 3, 329–342 (1961).

    Google Scholar 

  13. M. N. A. Newman, “On theories with a combinatorial definition of ‘equivalence’,” Ann. Math.,43, No. 2, 223–243 (1942).

    Google Scholar 

  14. H. Barendrecht, Lambda-Computation, Its Syntax and Semantics [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  15. J. Peterson, “The word problem in absorbing varieties,” Houston J. Math.,11, No. 4, 575–590 (1985).

    Google Scholar 

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Authors
  1. L. V. Shabunin
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Cheboksary. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 201–211, May–June, 1991.

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Shabunin, L.V. On decidability of theories of finitely generated quasigroups in R-varieties of groups. Sib Math J 32, 522–532 (1991). https://doi.org/10.1007/BF00970492

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