Bouligand–Severi tangents in MV-algebras
Manuela Busaniche, Daniele Mundici · Revista Matemática Iberoamericana · 2014
In their important recent paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra A strongly semisimple if all principal quotients of A 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 A is strongly semisimple if and only if its maximal spectral space \mu(A)\subseteq [0,1]^2 does not have any rational Bouligand–Severi tangents at its rational points. In general, when A is finitely generated and \mu(A)\subseteq [0,1]^n has a Bouligand–Severi tangent then A is not strongly semisimple. An MV-algebra A is strongly semisimple if and only if so is every 2-generator subalgebra of A .