A constructive proof that every 3-generated l-group is ultrasimplicial
Mundici, Daniele ; Panti, Giovanni
Banach Center Publications, Tome 50 (1999), p. 169-178 / Harvested from The Polish Digital Mathematics Library
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We discuss the ultrasimplicial property of lattice-ordered abelian groups and their associated MV-algebras. We give a constructive proof of the fact that every lattice-ordered abelian group generated by three elements is ultrasimplicial.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:208920 
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     author = {Mundici, Daniele and Panti, Giovanni},
     title = {A constructive proof that every 3-generated l-group is ultrasimplicial},
     journal = {Banach Center Publications},
     volume = {50},
     year = {1999},
     pages = {169-178},
     zbl = {1002.06014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv46i1p169bwm}
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Mundici, Daniele; Panti, Giovanni. A constructive proof that every 3-generated l-group is ultrasimplicial. Banach Center Publications, Tome 50 (1999) pp. 169-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv46i1p169bwm/

[000] [BML67] G. Birkhoff and S. Mac Lane, Algebra. The Macmillan Co., New York, 1967.

[001] [Cha58] C. C. Chang, Algebraic analysis of many valued logics. Trans. Amer. Math. Soc., 88:467-490, 1958. | Zbl 0084.00704

[002] [Ell79] G. Elliott, On totally ordered groups, and K0. In Ring Theory (Proc. Conf. Univ. Waterloo, Waterloo, 1978), volume 734 of Lecture Notes in Math., pages 1-49. Springer, 1979.

[003] [Ewa96] G. Ewald, Combinatorial Convexity and Algebraic Geometry. Springer, 1996.

[004] [Ful93] W. Fulton, An introduction to Toric Varieties, volume 131 of Annals of Mathematics Studies. Princeton University Press, Princeton, N.J., 1993.

[005] [Han83] D. Handelman, Ultrasimplicial dimension groups. Arch. Math., 40:109-115, 1983. | Zbl 0513.46049

[006] [MP93] D. Mundici and G. Panti, The equivalence problem for Bratteli diagrams. Technical Report 259, Department of Mathematics, University of Siena, Siena, Italy, 1993.

[007] [Mun86] D. Mundici, Interpretation of AF C*-algebras in Łukasiewicz sentential calculus. J. of Functional Analysis, 65:15-63, 1986. | Zbl 0597.46059

[008] [Mun88] D. Mundici, Farey stellar subdivisions, ultrasimplicial groups, and K0 of AF C*-algebras. Advances in Math., 68(1):23-39, 1988. | Zbl 0678.06008

[009] [Oda88] T. Oda, Convex Bodies and Algebraic Geometry. Springer, 1988.