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On weak direct product decompositions of lattices and graphs. (English) Zbl 0576.06006

The author continues his investigation of lattices determined by their graphs [see Czech. Math. J. 34(109), 305-314 (1984; Zbl 0557.06004)]. The main results concern the class \(C_ 0\) of these lattices: \(C_ 0\) is closed with respect to weak direct products (i.e. to finite direct products, consequently), any lattice is a sublattice of a member of \(C_ 0\), a lattice belongs to \(C_ 0\) iff all its directly indecomposable direct factors belong to \(C_ 0\).
Reviewer: J.Rosicky

MSC:

06B05 Structure theory of lattices
06B15 Representation theory of lattices
05C99 Graph theory

Citations:

Zbl 0557.06004
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References:

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