Pavel R\accent 23u\v zi\v cka

Pavel R\accent 23u\v zi\v cka
Countable chains of distributive lattices as maximal semilattice quotients of positive cones of dimension groups

Comment.Math.Univ.Carolinae 47,1 (2006) 11-20.

Abstract:We construct a countable chain of Boolean semilattices, with all inclusion maps preserving the join and the bounds, whose union cannot be represented as the maximal semilattice quotient of the positive cone of any dimension group. We also construct a similar example with a countable chain of strongly distributive bounded semilattices. This solves a problem of F. Wehrung.

Keywords: semilattice, lattice, distributive, dimension group, direct limit
AMS Subject Classification: 06A12, 06B15, 06D05, 06F20, 20K25

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Pavel R\accent 23u\v zi\v cka Countable chains of distributive lattices as maximal semilattice quotients of positive cones of dimension groups

Pavel R\accent 23u\v zi\v cka
Countable chains of distributive lattices as maximal semilattice quotients of positive cones of dimension groups