Negation operations definable on finite distributive lattices

Priestley, H.A.; Bordalo, G.

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

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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. ...

Varieties of Distributive Rotational Lattices

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A rotational lattice is a structure $〈 L; \lor, \land, g 〉$ where $L = 〈 L; \lor, \land 〉$ is a lattice and $g$ is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices.

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