Some remarks concerning the varieties generated by the diamond and the pentagon
HTML articles powered by AMS MathViewer
- by S. D. Comer and D. X. Hong PDF
- Trans. Amer. Math. Soc. 174 (1972), 45-54 Request permission
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
- Bjarni Jónsson, Equational classes of lattices, Math. Scand. 22 (1968), 187–196 (1969). MR 246797, DOI 10.7146/math.scand.a-10882
- Ralph McKenzie, Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc. 174 (1972), 1–43. MR 313141, DOI 10.1090/S0002-9947-1972-0313141-1
- Maurice-Paul Schützenberger, Sur certains axiomes de la théorie des structures, C. R. Acad. Sci. Paris 221 (1945), 218–220 (French). MR 14058
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 174 (1972), 45-54
- MSC: Primary 06A20
- DOI: https://doi.org/10.1090/S0002-9947-1972-0313142-3
- MathSciNet review: 0313142