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Affine representations of \({\ell}\)-groups and MV-algebras

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Abstract

Affine representations for archimedean \({\ell}\)-groups and semisimple MV-algebras via embedding theorems are presented; they are simple to work with but powerful enough to express significant properties of our studied objects. Indeed, we focus on the space of particular homomorphisms between an archimedean \({\ell}\)-group (a semisimple MV-algebra, respectively) and a vector lattice (a Riesz MV-algebra, respectively), i.e., the set of the generalized states, providing a general framework.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Perugia, Via Vanvitelli 1, I-06123, Perugia (PG), Italy

    Antonio Boccuto

  2. Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132, I-84084, Fisciano (SA), Italy

    Antonio Di Nola & Gaetano Vitale

Authors
  1. Antonio Boccuto
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  2. Antonio Di Nola
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  3. Gaetano Vitale
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Correspondence to Gaetano Vitale.

Additional information

Presented by S. Pulmannova.

Antonio Boccuto gratefully acknowledges the support from University of Perugia and the G.N.A.M.P.A. (the Italian National Group of Mathematical Analysis, Probability and Applications). Our thanks to Prof. Giacomo Lenzi and to the anonymous referee for their helpful suggestions.

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Boccuto, A., Di Nola, A. & Vitale, G. Affine representations of \({\ell}\)-groups and MV-algebras. Algebra Univers. 78, 563–577 (2017). https://doi.org/10.1007/s00012-017-0477-5

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  • DOI: https://doi.org/10.1007/s00012-017-0477-5

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