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arXiv · 1309.7525

Isoform lattices

G. Grätzer·E. T. Schmidt·R. W. Quackenbush
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Abstract

Let $L$ be a lattice. We call a congruence relation $\gQ$ of $L$ isoform, if any two congruence classes of $\gQ$ are isomorphic (as lattices). Let us call the lattice $L$ isoform, if all congruences of $L$ are isoform. G. Grätzer and E.\,T. Schmidt proved that every finite distributive lattice $D$ can be represented as the congruence lattice of a finite isoform lattice $L$. We now prove that every finite lattice $K$ has a congruence-preserving extension to a finite isoform lattice $L$.

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G. Grätzer, E. T. Schmidt, R. W. Quackenbush. 2013-09-29. Isoform lattices. https://arxiv.org/abs/1309.7525

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