Directly indecomposable direct factors of a lattice. (English) Zbl 0879.06002

Jakubík, J.

Math. Bohem. 121, No. 3, 281-292 (1996).

A lattice is called a \(V_1\)-lattice if every element is the join of strictly join-irreducible elements. L. Libkin [Algebra Univers. 33, No.1, 127-135 (1995; Zbl 0818.06004)] proved that every algebraic \(V_1\)-lattice is a direct product of directly indecomposable lattices. In the paper under review, the author generalizes this result for conditionally complete and orthogonally complete compactly generated \(V_1\)-lattices with 0.

Reviewer: J.Rachůnek (Olomouc)

MSC:

06B05

Structure theory of lattices

Keywords:

direct product of lattices; algebraic lattice; strictly irreducible element