Congruence-preserving extensions of finite lattices to sectionally complemented lattices |
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| Authors: | G. Grä tzer E. T. Schmidt |
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| Affiliation: | Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 ; Mathematical Institute of the Technical University of Budapest, Muegyetem rkp.~3, H-1521 Budapest, Hungary |
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| Abstract: | In 1962, the authors proved that every finite distributive lattice can be represented as the congruence lattice of a finite sectionally complemented lattice. In 1992, M. Tischendorf verified that every finite lattice has a congruence-preserving extension to an atomistic lattice. In this paper, we bring these two results together. We prove that every finite lattice has a congruence-preserving extension to a finite sectionally complemented lattice. |
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| Keywords: | Congruence lattice congruence-preserving embedding sectionally complemented lattice finite |
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