In their important recent paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra strongly semisimple if all principal quotients of 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 is strongly semisimple if and only if its maximal spectral space does not have any rational Bouligand–Severi tangents at its rational points. In general, when is finitely generated and has a Bouligand–Severi tangent then is not strongly semisimple. An MV-algebra is strongly semisimple if and only if so is every 2-generator subalgebra of .
Cite this article
Manuela Busaniche, Daniele Mundici, Bouligand–Severi tangents in MV-algebras. Rev. Mat. Iberoam. 30 (2014), no. 1, pp. 191–201DOI 10.4171/RMI/774