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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0313142-3
PII: S 0002-9947(1972)0313142-3
Keywords: Variety of lattices, equational base, Schützenberger identities, modular law, distributive law
Article copyright: © Copyright 1972 American Mathematical Society