Bouligand-Severi Tangents in MV-Algebras

Manuela Busaniche; Daniele Mundici

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arXiv · 1204.2147

Bouligand-Severi Tangents in MV-Algebras

Manuela Busaniche·Daniele Mundici

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Abstract

In their recent seminal 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 m(A) does not have any rational Bouligand-Severi tangents at its rational points. In general, when A is finitely generated and m(A) has a Bouligand-Severi tangent then A is not strongly semisimple.

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BibTeX RIS

Manuela Busaniche, Daniele Mundici. 2012-04-10. Bouligand-Severi Tangents in MV-Algebras. https://arxiv.org/abs/1204.2147

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