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A property of the lattice of equational theories. (English) Zbl 0604.08003

Author’s summary: It has been conjectured that any algebraic lattice having a compact one could be represented as the lattice of equational theories extending some theory. However, we show that each lattice having such a representation satisfies a nontrivial quasidistributivity condition. In particular, \(M_ 3\) has no such representation.
Reviewer: E.Nelson

MSC:

08B15 Lattices of varieties
06B15 Representation theory of lattices
03C05 Equational classes, universal algebra in model theory
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References:

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