Finitely presented lattices: canonical forms and the covering relation

Freese, Ralph

doi:10.1090/S0002-9947-1989-0949899-0

Finitely presented lattices: canonical forms and the covering relation
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Trans. Amer. Math. Soc. 312 (1989), 841-860 Request permission

Abstract:

A canonical form for elements of a lattice freely generated by a partial lattice is given. This form agrees with Whitman’s canonical form for free lattices when the partial lattice is an antichain. The connection between this canonical form and the arithmetic of the lattice is given. For example, it is shown that every element of a finitely presented lattice has only finitely many minimal join representations and that every join representation can be refined to one of these. An algorithm is given which decides if a given element of a finitely presented lattice has a cover and finds them if it does. An example is given of a nontrivial, finitely presented lattice with no cover at all.

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