Direct decompositions of non-algebraic complete lattices. (English) Zbl 1023.06006
A bounded lattice \(L\) is said to be finitely bi-spatial if any element of \(L\) is a join of irreducible elements of \(L\), and dually. The main result of the paper is the following theorem: Every finitely bi-spatial lattice is isomorphic to a direct product of directly indecomposable lattices. The result is illustrated by a few examples and counterexamples.
Reviewer: Václav Slavík (Praha)