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In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.

Let $L$ be a lattice. In this paper, corresponding to a given congruence relation $\Theta$ of $L$, a congruence relation ${\Psi }_{\Theta }$ on $CS\left(L\right)$ is defined and it is proved that 1. $CS(L/\Theta )$ is isomorphic to $CS\left(L\right)/{\Psi }_{\Theta }$; 2. $L/\Theta$ and $CS\left(L\right)/{\Psi }_{\Theta }$ are in the same equational class; 3. if $\Theta$ is representable in $L$, then so is ${\Psi }_{\Theta }$ in $CS\left(L\right)$.

G. Szász, J. Szendrei, K. Iseki and J. Nieminen have made an extensive study of derivations and translations on lattices. In this paper, the concepts of meet-translations and derivations have been studied in trellises (also called weakly associative lattices or WA-lattices) and several results in lattices are extended to trellises. The main theorem of this paper, namely, that every derivatrion of a trellis is a meet-translation, is proved without using associativity and it generalizes a well-known...

This paper gives some new characterizations of completeness for trellises by introducing the notion of a cycle-complete trellis. One of our results yields, in particular, a characterization of completeness for trellises of finite length due to K. Gladstien (see K. Gladstien: Characterization of completeness for trellises of finite length, Algebra Universalis 3 (1973), 341–344).