Studia Logica 104 (2):185-208 (2016)

Abstract
An equivalence between the category of MV-algebras and the category $${{\rm MV^{\bullet}}}$$ MV ∙ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations $${a = \neg \neg a, \vee = 1}$$ a = ¬ ¬ a, ∨ = 1 and $${a \odot = a \wedge b}$$ a ⊙ = a ∧ b. An object of $${{\rm MV^{\bullet}}}$$ MV ∙ is a residuated lattice which in particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where A is an MV-algebra and I is an ideal of A.
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DOI 10.1007/s11225-015-9632-1
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References found in this work BETA

On the Representation of N4-Lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.
Nelson Algebras Through Heyting Ones: I.Andrzej Sendlewski - 1990 - Studia Logica 49 (1):105-126.
Dualities for Modal N4-Lattices.R. Jansana & U. Rivieccio - 2014 - Logic Journal of the IGPL 22 (4):608-637.

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