Almost distributive sublattices and congruence heredity

Author: Snow John  

Publisher: Springer Publishing Company

ISSN: 0002-5240

Source: algebra universalis, Vol.57, Iss.1, 2007-08, pp. : 3-14

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Abstract

A congruence lattice L</b> of an algebra A</b> is hereditary if every 0-1 sublattice of L</b> is the congruence lattice of an algebra on A</i>. Suppose that L</b> is a finite lattice obtained from a distributive lattice by doubling a convex subset. We prove that every congruence lattice of a finite algebra isomorphic to L</b> is hereditary.