The \(M_3[D]\) construction and \(n\)-modularity (Q5932470)

In 1968, \textit{E. T. Schmidt} [Mat. Čas. Sloven. Akad. Vied 18, 3-20 (1968; Zbl 0155.35102)] introduced the \(M_3[D]\) construction, an extension of the five-element modular nondistributive lattice \(M_3\) by a bounded distributive lattice \(D\), defined as a lattice of all triples \(\langle x,y,z\rangle \in D^3\) with \(x\wedge y = x \wedge z = y \wedge z\). He has shown that \(M_3[D]\) is a modular congruence preserving extension of \(D\).