Geodesic
On Axioms for Semi-Lattices
Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 357-358

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By a semi-lattice we mean a system <L,.> where L is a set and. is a binary operation in L that is idempotent, commutative and associative. In a recent article [2] D.H. Potts considers the problem of reducing the number of axioms for a semi-lattice. His result was that the following two axioms viz. (1) xx=x, (2) (uv)((wx)(yz)) = ((uv)(xw))(zy) are sufficient to give a semi-lattice. But the second identity contains six elements instead of the original three. In the following we give a set of two simple identities with just three elements for a semi-lattice. This improves the above mentioned result. 
Padmanabhan, R. On Axioms for Semi-Lattices. Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 357-358. doi: 10.4153/CMB-1966-046-9
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     title = {On {Axioms} for {Semi-Lattices}},
     journal = {Canadian mathematical bulletin},
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     year = {1966},
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     doi = {10.4153/CMB-1966-046-9},
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