Růžička, Pavel A distributive semilattice not isomorphic to the maximal semilattice quotient of the positive cone of any dimension group. (English) Zbl 1025.06003 J. Algebra 268, No. 1, 290-300 (2003). Summary: We construct a distributive 0-semilattice which is not isomorphic to the maximal semilattice quotient of the positive cone of any dimension group. The size of the semilattice is \({\aleph}_2\). Cited in 1 ReviewCited in 3 Documents MSC: 06A12 Semilattices Keywords:distributive semilattice; semilattice quotient; positive cone; dimension group PDF BibTeX XML Cite \textit{P. Růžička}, J. Algebra 268, No. 1, 290--300 (2003; Zbl 1025.06003) Full Text: DOI References: [1] G.M. Bergman, Von Neumann regular rings with tailor-made ideal lattices, Unpublished notes, 1986 [2] Effros, E.G.; Handelman, D.E.; Shen, C.-L., Dimension groups and their affine representations, Amer. J. math., 120, 385-407, (1980) · Zbl 0457.46047 [3] Goodearl, K.R., Partially ordered abelian groups with interpolation, Math. surveys monogr., 20, (1986), Amer. Math. Soc Providence, RI · Zbl 0589.06008 [4] Goodearl, K.R.; Handelman, D.E., Tensor product of dimension groups and K0 of unitregular rings, Canad. J. math., 38, 633-658, (1986) · Zbl 0608.16027 [5] Goodearl, K.R.; Wehrung, F., Representations of distributive semilattice in ideal lattices of various algebraic structures, Algebra universalis, 45, 71-102, (2001) · Zbl 1039.06003 [6] Grätzer, K.R., General lattice theory, (1998), Birkhäuser Basel [7] P. Růžička, Representation of distributive lattices by semilattices of finitely generated ideals of locally matricial algebras, Preprint, 1999 [8] J. Tůma, F. Wehrung, Liftings of diagrams of semilattices by diagrams of dimension groups, Proc. London Math. Soc., in press · Zbl 1040.06002 [9] Wehrung, F., Non-measurability properties of interpolation vector spaces, Israel J. math., 103, 177-206, (1998) · Zbl 0916.06018 [10] Wehrung, F., A uniform refinement property for congruence lattices, Proc. amer. math. soc., 127, 363-370, (1999) · Zbl 0902.06006 [11] Wehrung, F., Representation of algebraic distributive lattices with \(ℵ1\) compact elements as ideal lattices of regular rings, Publ. mat., 44, 419-435, (2000) · Zbl 0989.16010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.