A constructive proof that every 3-generated l-group is ultrasimplicial

Daniele Mundici; Giovanni Panti

Banach Center Publications (1999)

  • Volume: 46, Issue: 1, page 169-178
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Mundici, Daniele, and Panti, Giovanni. "A constructive proof that every 3-generated l-group is ultrasimplicial." Banach Center Publications 46.1 (1999): 169-178. <http://eudml.org/doc/208920>.

@article{Mundici1999,
abstract = {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.},
author = {Mundici, Daniele, Panti, Giovanni},
journal = {Banach Center Publications},
keywords = {ultrasimplicially ordered group; lattice-ordered abelian groups; simplicially ordered groups; fans; subdivision; starrings; cones},
language = {eng},
number = {1},
pages = {169-178},
title = {A constructive proof that every 3-generated l-group is ultrasimplicial},
url = {http://eudml.org/doc/208920},
volume = {46},
year = {1999},
}

TY - JOUR
AU - Mundici, Daniele
AU - Panti, Giovanni
TI - A constructive proof that every 3-generated l-group is ultrasimplicial
JO - Banach Center Publications
PY - 1999
VL - 46
IS - 1
SP - 169
EP - 178
AB - 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.
LA - eng
KW - ultrasimplicially ordered group; lattice-ordered abelian groups; simplicially ordered groups; fans; subdivision; starrings; cones
UR - http://eudml.org/doc/208920
ER -

References

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  1. [BML67] G. Birkhoff and S. Mac Lane, Algebra. The Macmillan Co., New York, 1967. 
  2. [Cha58] C. C. Chang, Algebraic analysis of many valued logics. Trans. Amer. Math. Soc., 88:467-490, 1958. Zbl0084.00704
  3. [Ell79] G. Elliott, On totally ordered groups, and K 0 . In Ring Theory (Proc. Conf. Univ. Waterloo, Waterloo, 1978), volume 734 of Lecture Notes in Math., pages 1-49. Springer, 1979. 
  4. [Ewa96] G. Ewald, Combinatorial Convexity and Algebraic Geometry. Springer, 1996. 
  5. [Ful93] W. Fulton, An introduction to Toric Varieties, volume 131 of Annals of Mathematics Studies. Princeton University Press, Princeton, N.J., 1993. 
  6. [Han83] D. Handelman, Ultrasimplicial dimension groups. Arch. Math., 40:109-115, 1983. Zbl0513.46049
  7. [MP93] D. Mundici and G. Panti, The equivalence problem for Bratteli diagrams. Technical Report 259, Department of Mathematics, University of Siena, Siena, Italy, 1993. 
  8. [Mun86] D. Mundici, Interpretation of AF C*-algebras in Łukasiewicz sentential calculus. J. of Functional Analysis, 65:15-63, 1986. Zbl0597.46059
  9. [Mun88] D. Mundici, Farey stellar subdivisions, ultrasimplicial groups, and K 0 of AF C*-algebras. Advances in Math., 68(1):23-39, 1988. Zbl0678.06008
  10. [Oda88] T. Oda, Convex Bodies and Algebraic Geometry. Springer, 1988. 

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