Skip to main content
Log in

Some algorithmic problems for projective planes

  • Published:
Algebra and Logic Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. A. I. Mal'tsev, "Model correspondences," Izv. Akad. Nauk SSSR, Ser. Mat.,23, No. 3, 313–336 (1959).

    Google Scholar 

  2. A. I. Mal'tsev, Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  3. A. I. Shirshov and A. A. Nikitin, "On the theory of projective planes," Algebra Logika,20, No. 3, 330–356 (1981).

    Google Scholar 

  4. A. A. Nikitin, "Homorphisms of freely generated projective planes," Algebra Logika,20, No. 4, 419–426 (1981).

    Google Scholar 

  5. A. A. Nikitin, "On freely generated projective planes," Algebra Logika,22, No. 1, 61–78 (1983).

    Google Scholar 

  6. H. Rogers, Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York-Toronto-London (1967).

    Google Scholar 

  7. L. A. Skornyakov, "Projective planes," Usp. Mat. Nauk,6, No. 6, 112–154 (1951).

    Google Scholar 

  8. M. Hall, Jr., The Theory of Groups, Macmillan, New York (1959).

    Google Scholar 

  9. P. M. Cohn, "The word problem for free fields," J. Symb. Logic,38, No. 2, 309–314 (1973).

    Google Scholar 

  10. P. M. Cohn, "The word problem for free fields: a correction and an addendum," J. Symb. Logic,40, No. 1, 69–74 (1975).

    Google Scholar 

  11. S. Foldes and N. Singhi, "A nonconstructive projective plane," Geom. Dedic.,9, No. 4, 497–499 (1980).

    Google Scholar 

  12. A. Givagnally, "Sulla rappresentazione di un piano libero mediante una classa di simboli," Rend. Mat. Applic.,25, No. 3–4, 427–432 (1966–1967).

    Google Scholar 

  13. M. Hall, Jr., "Projective planes," Trans. Am. Math. Soc.,54, 229–277 (1943).

    Google Scholar 

  14. M. Hall, Jr., "Correction to ‘Projective planes’," Trans. Am. Math. Soc.,65, No. 3, 473–474 (1949).

    Google Scholar 

  15. D. R. Hughes and F. C. Piper, Projective Planes, 2nd edn., Springer-Verlag, New York (1982).

    Google Scholar 

  16. K. H. Kim and F. W. Roush, "A universal algebra approach to free projective planes," Aequat. Math.,18, No. 3, 399–400 (1978).

    Google Scholar 

  17. K. H. Kim and F. W. Roush, "A universal algebra approach to free projective planes," Aequat. Math.,19, No. 1, 48–52 (1979).

    Google Scholar 

  18. L. Lipshitz, "The undecidability of the word problem for projective geometries and modular lattices," Trans. Am. Math. Soc.,193, No. 1, 171–180, 1974.

    Google Scholar 

  19. R. Magari, "Su una classa di simboli atta a rappresentare gli elementi di un piano grafico e su un theorema di ridizione a forma normale," Atti Naz. Lincei Rend. Cl. Sci. Fiz. Mat. Natur.,33, No. 1–2, 37–44 (1962).

    Google Scholar 

  20. A. MacIntyre, "The word problem for division rings," J. Symb. Logic,38, No. 3, 428–436 (1973).

    Google Scholar 

  21. A. MacIntyre, "Combinatorial problems for skew fields. I, Analogue of Britton's lemma and results of Adjan-Rabin type," Proc. London Math. Soc.,39, No. 2, 211–236 (1979).

    Google Scholar 

  22. G. Pickert, Projektive Ebenen, 2nd edn., Springer-Verlag, Berlin-New York (1975).

    Google Scholar 

  23. H. Simmons, "The solution of a decision problem for several classes of rings," Pac. J. Math.,34, No. 2, 547–557 (1970).

    Google Scholar 

  24. A. Schmidt, "Über deduktive Theorien mit mehreren Sorten von Grunddingen," Math. Ann.,115, 485–506 (1938).

    Article  Google Scholar 

  25. A. Schmidt, "Die Zulässigkeit der Behandlung mehrsortiger Theorien mittels der üblichen einsortigen Prädikatenlogik," Math. Ann.,123, 187–200 (1951).

    Google Scholar 

Download references

Authors

Additional information

Translated from Algebra i Logika, Vol. 23, No. 5, pp. 512–529, September–October, 1984.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikitin, A.A. Some algorithmic problems for projective planes. Algebra and Logic 23, 347–358 (1984). https://doi.org/10.1007/BF01982028

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01982028

Keywords

Navigation