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The lattice of convex sublattices of a lattice. (Russian) Zbl 0711.06005
For a lattice L let Sub L and CSub L be the lattice of all sublattices of L or the lattice of all convex sublattices of L, respectively (including the empty set). The author is interested in the question to what extent the lattice L is determined by CSub L. Typical results: Let L and \(L'\) be lattices; then CSub \(L\simeq CSub L'\) iff there exists a bijection f: \(L\to L'\) such that \(f([a\wedge b,a\vee b])=[f(a)\wedge f(b),f(a)\vee f(b)]\) for each a,b\(\in L\). Let L be a discrete modular lattice; then L is determined up to isomorphism by CSub L iff some of the following conditions is valid: (i) each direct factor of L is selfdual; (ii) each directly indecomposable direct factor of L is selfdual. Next, the author investigates the relations between the groups of automorphisms of the lattices L, Conv L and CSub L.
Reviewer: J.JakubĂ­k

MSC:
06B05 Structure theory of lattices
06C05 Modular lattices, Desarguesian lattices
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