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Algebraic geometry for \(\ell \)-groups

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In this paper we focus on the algebraic geometry of the variety of \(\ell \)-groups (i.e. lattice ordered abelian groups). In particular we study the role of the introduction of constants in functional spaces and \(\ell \)-polynomial spaces, which are themselves \(\ell \)-groups, evaluated over other \(\ell \)-groups. We use different tools and techniques, with an increasing level of abstraction, to describe properties of \(\ell \)-groups, topological spaces (with the Zariski topology) and a formal logic, all linked by the underlying theme of solutions of \(\ell \)-equations.

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Authors and Affiliations

  1. Mathematics Department, University of Salerno, Via Giovanni Paolo II 132, 84084, Fisciano, SA, Italy

    Antonio Di Nola, Giacomo Lenzi & Gaetano Vitale

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  1. Antonio Di Nola
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  2. Giacomo Lenzi
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  3. Gaetano Vitale
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Correspondence to Giacomo Lenzi.

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Di Nola, A., Lenzi, G. & Vitale, G. Algebraic geometry for \(\ell \)-groups. Algebra Univers. 79, 64 (2018). https://doi.org/10.1007/s00012-018-0548-2

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