Representing homomorphisms of distributive lattices as restrictions of congruences of rectangular lattices |
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Authors: | Email author" target="_blank">Gábor?CzédliEmail author |
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Institution: | 1.University of Szeged, Bolyai Institute,Szeged,Hungary |
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Abstract: | Let be a {0, 1}-homomorphism of a finite distributive lattice D into the congruence lattice Con L of a rectangular (whence finite, planar, and semimodular) lattice L. We prove that L is a filter of an appropriate rectangular lattice K such that ConK is isomorphic with D and is represented by the restriction map from Con K to Con L. The particular case where is an embedding was proved by E.T. Schmidt. Our result implies that each {0, 1}-lattice homomorphism between two finite distributive lattices can be represented by the restriction of congruences of an appropriate rectangular lattice to a rectangular filter. |
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