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Directly indecomposable direct factors of a lattice. (English) Zbl 0879.06002
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.
MSC:
06B05 Structure theory of lattices
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