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Pavel R˚uˇziˇcka +KJ=>A ?D=EI B @EIJHE>KJELA =JJE?AI =I =NE= IAE=J JE?A GKJEAJI B FIEJELA ?AI B @EAIE CHKFI

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Pavel R˚ uˇ ziˇ cka

Countable chains of distributive lattices as maximal semilat- tice 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 inclu- sion 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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