Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4597954 | Journal of Pure and Applied Algebra | 2008 | 10 Pages |
Abstract
We present two examples of distributive algebraic lattices which are not isomorphic to the congruence lattice of any lattice. The first such example was discovered by F. Wehrung in 2005. One of our examples is defined topologically, the other one involves majority algebras. In particular, we prove that the congruence lattice of the free majority algebra on (at least) âµ2 generators is not isomorphic to the congruence lattice of any lattice. Our method is a generalization of Wehrung's approach, so that we are able to apply it to a larger class of distributive semilattices.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Miroslav PloÅ¡Äica,