Congruence Class Sizes in Finite Sectionally Complemented Lattices

Canadian mathematical bulletin

关键词: congruence lattice;    congruence-preserving extension;   

DOI  :  10.4153/CMB-2004-019-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

The congruences of a finite sectionally complemented lattice $L$ arenot necessarily emph{uniform} (any two congruence classes of acongruence are of the same size). To measure how far a congruence$Theta$ of $L$ is from being uniform, we introduce $SpecTheta$, theemph{spectrum} of $Theta$, the family of cardinalities of thecongruence classes of $Theta$. A typical result of this papercharacterizes the spectrum $S = (m_j mid j < n)$ of a nontrivialcongruence $Theta$ with the following two properties:egin{enumerate}[$(S_2)$]item[$(S_1)$] $2 leq n$ and $n eq 3$.item[$(S_2)$] $2 leq m_j$ and $m_j eq 3$, for all $j

【 授权许可】

Unknown