Title: n-DISTRIBUTIVITY AND SOME QUESTIONS OF THE EQUATIONAL THEORY OF LATTICES
Abstract: This chapter presents the concept of n-distributivity and some questions of the equational theory of lattices. The chapter presents some results on n-distributive lattices and (n + l)-frames to give new counterexamples (and new proofs of already known counterexamples) concerning some questions of the theory of varieties of lattices. Among others, it constructs lattice varieties which are not generated by their finite members, which cannot be defined by finitely many equations, etc. The proofs are of a purely lattice theoretic nature. They use only notions but no theorems from universal algebra, and the only model theoretic fact needed is the compactness theorem in the proof of a corollary. The chapter also describes a sublattice of the lattice Δ of lattice varieties. The two basic tools are Jonsson's lemma and Birkhoff's characterization of the free distributive lattice generated by two chains.
Publication Year: 1977
Publication Date: 1977-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 9
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