Inherently nonfinitely based finite algebras

  • George F. McNulty
  • Caroline R. Shallon
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1004)

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§6 References

  1. 1.
    Garrett Birkhoff, On the structure of abstract algebras, Proc. Cambridge Phil. Soc. 31 (1935) 433–454.CrossRefMATHGoogle Scholar
  2. 2.
    Roger Bryant, The laws of finite pointed groups, Bull. London Math. Soc., to appear.Google Scholar
  3. 3.
    Stanley Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York, 1981, 276 pp. + xvi.CrossRefMATHGoogle Scholar
  4. 4.
    Roger Lyndon, Identities in finite algebras, Proc. Amer. Math. Soc. 5 (1954) 8–9.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Charles Martin, Equational theories of natural numbers and transfinite ordinals, Ph.D. thesis, U. C. Berkeley, 1973, 213 pp. + xvi.Google Scholar
  6. 6.
    Ralph McKenzie, Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties, Algebra Universal 8 (1978) 336–348.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Ralph McKenzie, A new product of algebras and a type reduction theorem, Algebra Universalis, to appear.Google Scholar
  8. 8.
    V. L. Murskii, The existence in three valued logic of a closed class with finite basis not having a finite complete set of identities, Dokl. Akad. Nauk. SSSR 163 (1965) 815–818; English transl. Soviet Math. Dokl. 6 (1965) 1020–1024.MathSciNetGoogle Scholar
  9. 9.
    V. L. Murskii, On the number of k-element algebras with one binary operation without a finite basis of identities, (Russian) Problemy Kibernet 35 (1979) 5–27.MathSciNetGoogle Scholar
  10. 10.
    Sheila Oates-MacDonald and Michael Vaughan-Lee, Varieties that make one Cross, J. Anstral. Math. Soc. (Series A) 26 (1978) 368–382.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Sheila Oates-Williams, Murskii's algebra does not satisfy min, Bull. Austral. Math. Soc. 22 (1980) 199–203.MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Robert Park, A four-element algebra whose identities are not finitely based, Algebra Universalis 11 (1980) 255–260.MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Peter Perkins, Bases for equational theories of semigroups, J. Algebra 11 (1969) 293–314.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Peter Perkins, Basis questions for general algebras, preprint.Google Scholar
  15. 15.
    Don Pigozzi, Finite groupoids without finite bases for their identities, Algebra Universalis 13 (1981).Google Scholar
  16. 16.
    S. V. Polin, On the identities of finite algebras, Sib. Math. J. 17 (1976) 1356–1366.MathSciNetGoogle Scholar
  17. 17.
    Caroline Shallon, Nonfinitely based finite algebras derived from lattices, Ph.D. Dissertation, U.C.L.A. 1979, 144 pp. + viii.Google Scholar
  18. 18.
    Michael Vaughan-Lee, Laws in finite loops, Algebra Universalis 9 (1979) 269–280.MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    V. V. Visin, Identical transformations in four-place logic, Dokl. Akad. Nauk. SSSR 150 (1963) 719–721.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • George F. McNulty
    • 1
    • 2
  • Caroline R. Shallon
    • 1
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of South CarolinaColumbia
  2. 2.Space Flight Mechanics DepartmentHughes Aircraft CorporationLos Angeles

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