JournalsrmiVol. 30, No. 1pp. 191–201

Bouligand–Severi tangents in MV-algebras

  • Manuela Busaniche

    Universidad Nacional del Litoral, Santa Fé, Argentina
  • Daniele Mundici

    Università degli Studi di Firenze, Italy
Bouligand–Severi tangents in MV-algebras cover
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Abstract

In their important recent paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra AA strongly semisimple if all principal quotients of AA are semisimple. All boolean algebras are strongly semisimple, and so are all finitely presented MV-algebras. We show that for any 1-generator MV-algebra, semisimplicity is equivalent to strong semisimplicity. Further, a semisimple 2-generator MV-algebra AA is strongly semisimple if and only if its maximal spectral space μ(A)[0,1]2\mu(A)\subseteq [0,1]^2 does not have any rational Bouligand–Severi tangents at its rational points. In general, when AA is finitely generated and μ(A)[0,1]n\mu(A)\subseteq [0,1]^n has a Bouligand–Severi tangent then AA is not strongly semisimple. An MV-algebra AA is strongly semisimple if and only if so is every 2-generator subalgebra of AA.

Cite this article

Manuela Busaniche, Daniele Mundici, Bouligand–Severi tangents in MV-algebras. Rev. Mat. Iberoam. 30 (2014), no. 1, pp. 191–201

DOI 10.4171/RMI/774