ACTA issues

Congruence lattices and cover-preserving embeddings of finite length semimodular lattices. I

E. Tamás Schmidt

Acta Sci. Math. (Szeged) 77:1-2(2011), 47-52

Abstract. Let ${\cal K}$ denote the class of finite length semimodular lattices that have congruence-determining chain ideals. Assume that $L\in{\cal K}$ and $D$ is a $(0,1)$-sublattice of $\mathop{\rm Con} L$. We prove the existence of an $\overline L\in{\cal K}$ such that $L$ is a filter of $\overline L$ and the restriction mapping from $\mathop{\rm Con} \overline L$ to $\mathop{\rm Con} L$ is an isomorphism from $\mathop{\rm Con} \overline L$ onto $D$. The particular case $D=\{0,1\} $, not only for $L\in{\cal K}$, has intensively been studied by several papers, including [4], [5], [2] and [7].

AMS Subject Classification (1991): 06C10, 06B15

Keyword(s): lattice, semimodular, finite length, congruence lattice, embedding

Received May 11, 2009, and in final form March 17, 2011. (Registered under 66/2009.)