Abstract
We provide a list of universal axioms for cubic algebras inside the variety of implication algebras. This list is shown to axiomatize the subvariety generated by cubic algebras.
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References
Abbott, J.C. Sets, Lattices, and Boolean Algebras Allyn and Bacon, Boston, MA, 1969.
Bennet, M.K. The face lattice of an n-dimensional cube Algebra Universalis 14 (1982), 82–86.
Birkhoff, G. Lattice Theory AMS Colloquium Publications, Vol.25, Providence RI, 1979.
Bailey, C.G. Free Cubic Algebras in preparation.
Bailey, C.G. and Oliveira, J.S. Cubic lattices preprint.
Chen, W.Y.C. and Oliveira, J.S. Implication Algebras and the Metropolis-Rota Axioms for Cubic Lattices preprint.
Metropolis, N. and Rota, G.-C. Combinatorial Structure of the Faces of the n-cube, SIAM J. Appl. Math 35 (1978), 689–694.
Oliveira, J.S. The Theory of Cubic Lattices Ph.D. thesis, MIT, 1992.
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© 1998 Birkhäuser
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Bailey, C., Oliveira, J. (1998). An Axiomization for Cubic Algebras. In: Sagan, B.E., Stanley, R.P. (eds) Mathematical Essays in honor of Gian-Carlo Rota. Progress in Mathematics, vol 161. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4108-9_16
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DOI: https://doi.org/10.1007/978-1-4612-4108-9_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8656-1
Online ISBN: 978-1-4612-4108-9
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