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The word and isomorphism problems in universal algebra

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Universal Algebra and Lattice Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1149))

The author wishes to thank the organising committee for its invitation to speak at the meeting, and especially S. D. Comer for making the meeting both stimulating and enjoyable. I wish to thank The Citadel, N.S.F. and Bowling Green State University Faculty Research Committee for funding.

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References

  1. S. I. Adian, On algorithmic problems in effectively complete classes of groups, Dokl. Akad. Nauk. SSSR, 123(1958), 13–16 (in Russian).

    MathSciNet  Google Scholar 

  2. W. M. Beynon, Applications of duality in the theory of finitely generated lattice-ordered abelian groups, Canad. J. Math., 24(1977), 243–254.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Bigard, K. Keimel and S. Wolfenstein, Groupes et anneaux réticulés, Lecture Notes in Math. 608 (Springer, Berlin 1977).

    MATH  Google Scholar 

  4. N. Blackburn, Conjugacy in nilpotent groups, Proc. Amer. Math. Soc., 16(1965), 143–148.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. W. Boone, The word problem, Ann. of Math., 70(1959), 207–265.

    Article  MathSciNet  MATH  Google Scholar 

  6. C. C. Chang and H. J. Keisler, Model Theory (N. Holland, Amsterdam 1973).

    MATH  Google Scholar 

  7. T. Evans, The word problem for abstract algebras, J. London Math. Soc., 26(1951), 64–71.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Evans, The isomorphism problem for some classes of multiplicative systems, Trans. Amer. Math. Soc., 109(1963), 303–312.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Freese, Free modular lattices, Trans. Amer. Math. Soc., 261(1980), 81–91.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. M. W. Glass, Countable lattice-ordered groups, Math. Proc. Cambridge Phil. Soc., 94(1983), 29–33.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. M. W. Glass, The isomorphism problem and undecidable properties for finitely presented lattice-ordered groups, Orders: description and roles, Ann. of Discrete Math. (ed. M. Pouzet and D. Richard), (N. Holland, Amsterdam 1984), pp. 157–170.

    Google Scholar 

  12. A. M. W. Glass, The universal theory of lattice-ordered abelian groups, (unpublished notes).

    Google Scholar 

  13. A. M. W. Glass and Y. Gurevich, The word problem for lattice-ordered groups, Trans. Amer. Math. Soc., 280(1983), 127–138.

    MathSciNet  MATH  Google Scholar 

  14. A. M. W. Glass and J. J. Madden, The word problem versus the isomorphism problem, J. London Math. Soc., 30(1984), 53–61.

    Article  MathSciNet  MATH  Google Scholar 

  15. Y. Gurevich and A. I. Kokorin, Universal equivalence of ordered abelian groups, Algebra i Logika, 2(1963), 37–39 (in Russian).

    MathSciNet  Google Scholar 

  16. C. Hermann, On the word problem for the modular lattice with four free generators, Math. Ann., 265(1983), 513–527.

    Article  MathSciNet  Google Scholar 

  17. V. M. Kopytov, Lattice-ordered locally nilpotent groups, Algebra and Logic, (14)4, 1975, 249–251.

    Article  MathSciNet  MATH  Google Scholar 

  18. N. G. Khisamiev, Universal theory of lattice-ordered abelian groups, Algebra i Logika, 5(1966), 71–76 (in Russian).

    MathSciNet  Google Scholar 

  19. R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Ergebnisse der Math. und ihrer Grenzgebiete, 89 (Springer, Berlin 1977).

    MATH  Google Scholar 

  20. W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory (Wiley, New York 1966).

    MATH  Google Scholar 

  21. A. A. Markov, On the impossibility of certain algorithms in the theory of associative systems, Dokl. Akad. Nauk. SSSR, 55(1947), 583–586.

    MathSciNet  Google Scholar 

  22. A. A. Markov, Insolubility of the problem of homeomorphy, Proc., International Congress of Math., 1958 (ed. J. A. Todd, University Press, Cambridge, 1960), pp. 300–306.

    Google Scholar 

  23. C. F. Miller III, On group-theoretic decision problems and their classification, Annals of Math. Studies 68 (University Press, Princeton, 1971).

    MATH  Google Scholar 

  24. P. S. Novikov, On the algorithmic unsolvability of the word problem in groups, Trudy Mat. Inst. Steklov, 44, 143, 1955 (in Russian).

    Google Scholar 

  25. E. L. Post, Recursive unsolvability of a problem of Thue, J. Symbolic Logic, 12(1947), 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  26. M. O. Rabin, Recursive unsolvability of group theoretic problems, Ann. of Math., 67(1958), 172–194.

    Article  MathSciNet  MATH  Google Scholar 

  27. H. Simmons, The solution of a decision problem of several classes of rings, Pacific J. Math., 34(1970), 547–557.

    Article  MathSciNet  MATH  Google Scholar 

  28. A. Urquhart, The undecidability of entailment and relevant implication, J. Symbolic Logic, 49(1984), 1059–1073.

    Article  MathSciNet  MATH  Google Scholar 

  29. E. C. Weinberg, Free lattice-ordered abelian groups I & II, Math. Ann., 151(1963), 187–199; ibid., 159(1965), 217–222.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Bowling Green State University, 43403, Bowling Green, Ohio

    A. M. W. Glass

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  1. A. M. W. Glass
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Stephen D. Comer

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© 1985 Springer-Verlag

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Glass, A.M.W. (1985). The word and isomorphism problems in universal algebra. In: Comer, S.D. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098459

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  • DOI: https://doi.org/10.1007/BFb0098459

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15691-8

  • Online ISBN: 978-3-540-39638-3

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