Strongly Algebraically Closed Cevian Lattices

Cevian operations on certain distributive lattices with zero were introduced by F. Wehrung in 2019, and they have been intensively studied since then. Algebraically closed and strongly algebraically closed lattices have been studied by J. Schmid and, in several papers, Czedli and author. In this note we introduce the notion of q^' -compactness for Cevian lattices and we characterize when a Cevian lattice is a strongly algebraically closed lattice. Also, we study properties of Cevian lattices. In particular, we obtain conditions that a Cevian lattice can be represented as the congruence lattice of a rectangular lattice.