Abstract
In 1904 Huntington [6] conjectured that every uniquely complemented lattice must be distributive (and hence a Boolean algebra). In 1945,R.P.Dilworth shattered this conjecture by proving that every lattice can be embedded in a uniquely complemented lattice [5]. Therefore, we consider making additional conditions on the uniquely complemented lattice, so that it is a distributive. Peirce’s theorem describes complemented lattice is distributive in the additional conditions. In this paper, we give another different proof of Peirce’s theorem in this paper, and consider its necessary and sufficient condition. In addition, we get equivalent conditions between uniquely complemented lattice and distributive from it.
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Song, L., Liu, H., Shu, Y. (2011). A Note on Peirce’s Theorem. In: Lin, S., Huang, X. (eds) Advances in Computer Science, Environment, Ecoinformatics, and Education. CSEE 2011. Communications in Computer and Information Science, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23357-9_71
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DOI: https://doi.org/10.1007/978-3-642-23357-9_71
Publisher Name: Springer, Berlin, Heidelberg
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