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Homomorphisms of Distributive Lattices as Restrictions of Congruences. II. Planarity and Automorphisms

Published online by Cambridge University Press:  20 November 2018

G. Grätzer  and
H. Lakser
G. Grätzer
Affiliation:
Department of Mathematics and Astronomy University of Manitoba Winnipeg, Manitoba R3T2N2
H. Lakser
Affiliation:
Department of Mathematics and Astronomy University of Manitoba Winnipeg, Manitoba R3T2N2
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Abstract

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We prove that any {0,1 }-preserving homomorphism of finite distributive lattices can be realized as the restriction of the congruence relations of a finite planar lattice with no nontrivial automorphisms to an ideal of that lattice, where this ideal also has no nontrivial automorphisms. We also prove that any {0,1 }-preserving homomorphism of finite distributive lattices with more than one element and any homomorphism of groups can be realized, simultaneously, as the restriction of the congruence relations and, respectively, the restriction of the automorphisms of a lattice L to those of an ideal of L; if the groups are both finite, then so is the lattice L.

Keywords

06B1006D9908A3008A35Latticecongruence latticeautomorphism group
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 1 , 01 February 1994 , pp. 3 - 54
Copyright
Copyright © Canadian Mathematical Society 1994

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