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On the relationship of AP, RS and CEP in congruence modular varieties. II


Authors: Clifford Bergman and Ralph McKenzie
Journal: Proc. Amer. Math. Soc. 103 (1988), 335-343
MSC: Primary 08B10; Secondary 03C25, 08B25, 20E06
DOI: https://doi.org/10.1090/S0002-9939-1988-0943041-2
MathSciNet review: 943041
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Abstract: Let $ V$ be a congruence distributive variety, or a congruence modular variety whose free algebra on 2 generators is finite. If $ V$ is residually small and has the amalgamation property, then it has the congruence extension property. Several applications are presented.


References [Enhancements On Off] (What's this?)

  • [1] C. Bergman, On the relationship of AP, RS and CEP in congruence modular varieties, Algebra Universalis 22 (1986), 164-171. MR 870465 (88g:08005)
  • [2] -, Another consequence of AP in residually small, congruence modular varieties, Houston J. Math. (to appear). MR 998447 (90i:08007)
  • [3] R. H. Bruck, A survey of binary systems, Springer-Verlag, New York, 1971. MR 0093552 (20:76)
  • [4] S. Burris and H. Sankappanavar, A course in universal algebra, Springer-Verlag, New York, 1981. MR 648287 (83k:08001)
  • [5] R. Freese and R. McKenzie, Residually small varieties with modular congruence lattices, Trans. Amer. Math. Soc. 264 (1981), 419-430. MR 603772 (83d:08012a)
  • [6] -, Commutator theory for congruence modular varieties, London Math. Soc. Lecture Notes Ser. 125, Cambridge Univ. Press, New York, 1987. MR 909290 (89c:08006)
  • [7] E. Kiss, Injectivity and related concepts in modular varieties I-II. Bull. Austral. Math. Soc. 32 (1985), 35-53.
  • [8] R. McKenzie, Narrowness implies uniformity, Algebra Universalis 15 (1982), 67-85. MR 663953 (83i:08003)
  • [9] R. McKenzie, G. McNulty and W. Taylor, Algebras, lattices, varieties, Volume I, Wadsworth & Brooks/Cole, Monterey, Calif., 1987. MR 883644 (88e:08001)
  • [10] H. Neumann, Varieties of groups, Springer-Verlag, Berlin, 1967. MR 0215899 (35:6734)
  • [11] R. W. Quackenbush, Varieties of Steiner loops and Steiner quasigroups, Canad. J. Math. 28, 1187-1198. MR 0424988 (54:12946)
  • [12] W. Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33-53. MR 0314726 (47:3278)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0943041-2
Article copyright: © Copyright 1988 American Mathematical Society

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