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Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

100%

Cabrer L., Celani S.

Open Mathematics

2006

tom 4

nr 4

600-623

In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.

Representation and duality for Hilbert algebras

81%

Celani S., Cabrer L., Montangie D.

Open Mathematics

2009

tom 7

nr 3

463-478

In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations. We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert space, are isomorphic. We explore how this duality is related to the duality given in [6] for finite Hilbert algebras, and with the topological duality developed in [7] for Tarski algebras.

Ograniczanie wyników

2 Open Mathematics

2 Cabrer L.

2 Celani S.

1 Montangie D.

1 2009

1 2006

Wyniki wyszukiwania

Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

Representation and duality for Hilbert algebras