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Transactions of the American Mathematical Society

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Some remarks concerning the varieties generated by the diamond and the pentagon

Authors: S. D. Comer and D. X. Hong
Journal: Trans. Amer. Math. Soc. 174 (1972), 45-54
MSC: Primary 06A20
MathSciNet review: 0313142
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Abstract: In 1945 M. P. Schützenberger exhibited two identities. He asserted that one provided an equational base for the diamond $ {M_3}$ and the other a base for the pentagon $ {N_5}$. Recently Ralph McKenzie produced another equational base for $ {N_5}$. In the present paper the authors modify McKenzie's idea to verify Schützenberger's assertion for $ {M_3}$. They also show Schützenberger's claim about $ {N_5}$ is false.

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

  • [1] B. Jónsson, Equational classes of lattices, Math. Scand. 22 (1968), 187-196. MR 40 #66. MR 0246797 (40:66)
  • [2] R. McKenzie, Equational bases and nonmodular lattices varieties, Trans. Amer. Math. Soc. 174 (1972), 1-43. MR 0313141 (47:1696)
  • [3] M. Schützenberger, Sur certains axiomes de la théorie des structures, C. R. Acad. Sci. Paris 221 (1945), 218-220. MR 7, 235. MR 0014058 (7:235d)

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Keywords: Variety of lattices, equational base, Schützenberger identities, modular law, distributive law
Article copyright: © Copyright 1972 American Mathematical Society

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