Congruence-preserving extensions of finite lattices to sectionally complemented lattices

Grätzer, G.; Schmidt, E.

doi:10.1090/S0002-9939-99-04671-7

Congruence-preserving extensions of finite lattices to sectionally complemented lattices
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by G. Grätzer and E. T. Schmidt PDF

Proc. Amer. Math. Soc. 127 (1999), 1903-1915 Request permission

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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