The Spectral and the Maximal Spectral Space

  • D. Mundici
Part of the Trends in Logic book series (TREN, volume 35)


Generalizing the construction of the Stone space of a boolean algebra, the set of prime ideals of every MV-algebra A is endowed with the hull-kernel (also known as Zariski, or spectral) topology. The resulting space is denoted spec(A). In contrast to the Stone space of a boolean algebra, spec(A) is generally not rich enough to uniquely characterize A up to isomorphism. Moreover, unless A is hyperarchimedean, spec(A) strictly contains the compact Hausdorff space.


Prime Ideal Boolean Algebra Maximal Ideal Compact Hausdorff Space Sheaf Representation 
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  1. 1.
    Bigard, A., Keimel, K., Wolfenstein, S. (1977). Groupes et Anneaux Réticulés. Lecture Notes in Mathematics (Vol. 608). Berlin: Springer.Google Scholar
  2. 2.
    Yosida, K. (1942). On the representation of the vector lattice. Proceedings of the Imperial Academy, Tokyo, 18, 339–343.CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Keimel, K. (1971). The representation of lattice-ordered groups and rings by sections in sheaves. Lecture Notes in Mathematics (Vol. 248). Berlin, Heidelberg, New York: Springer, pp.1–98.Google Scholar
  4. 4.
    Dubuc, E. J., Poveda, Y. (2010). Representation theory of MV-algebras. Annals of Pure and Applied Logic, 161, 1024–1046.Google Scholar
  5. 5.
    Yang, Yi Chuan, \({\ell}\) -groups and Bézout domains, Thesis, University of Stuttgart. Available at Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics “Ulisse Dini”University of FlorenceFlorenceItaly

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