Canadian Mathematical Society
Canadian Mathematical Society
  location:  Publicationsjournals
Search results

Search: MSC category 06B10 ( Ideals, congruence relations )

  Expand all        Collapse all Results 1 - 2 of 2

1. CMB 2004 (vol 47 pp. 191)

Grätzer, G.; Schmidt, E. T.
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)

Grätzer, G.; Lakser, H.; Schmidt, E. T.
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

© Canadian Mathematical Society, 2017 :