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1. CMB 2004 (vol 47 pp. 191)
Congruence Class Sizes in Finite Sectionally Complemented Lattices The congruences of a finite sectionally complemented lattice $L$ are
not necessarily \emph{uniform} (any two congruence classes of a
congruence are of the same size). To measure how far a congruence
$\Theta$ of $L$ is from being uniform, we introduce $\Spec\Theta$, the
\emph{spectrum} of $\Theta$, the family of cardinalities of the
congruence classes of $\Theta$. A typical result of this paper
characterizes the spectrum $S = (m_j \mid j < n)$ of a nontrivial
congruence $\Theta$ with the following two properties:
\begin{enumerate}[$(S_2)$]
\item[$(S_1)$] $2 \leq n$ and $n \neq 3$.
\item[$(S_2)$] $2 \leq m_j$ and $m_j \neq 3$, for all $j Keywords:congruence lattice, congruence-preserving extension Categories:06B10, 06B15 |
2. CMB 1998 (vol 41 pp. 290)
Congruence lattices of finite semimodular lattices We prove that every finite distributive lattice can be represented
as the congruence lattice of a finite (planar) {\it semimodular}
lattice.
Categories:06B10, 08A05 |