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Displaying similar documents to “A duality between unary algebras and their subuniverse lattices”

Stone Lattices

Adam Grabowski (2015)

Formalized Mathematics

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The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the...

Varieties of Distributive Rotational Lattices

Gábor Czédli, Ildikó V. Nagy (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A rotational lattice is a structure 〈 L ; ∨ , ∧ , g 〉 where L = 〈 L ; ∨ , ∧ 〉 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.

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

Leonardo Cabrer, Sergio Celani (2006)

Open Mathematics

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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. ...

On connections between hypergraphs and algebras

Konrad Pióro (2000)

Archivum Mathematicum

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The aim of the present paper is to translate some algebraic concepts to hypergraphs. Thus we obtain a new language, very useful in the investigation of subalgebra lattices of partial, and also total, algebras. In this paper we solve three such problems on subalgebra lattices, other will be solved in [[Pio4]]. First, we show that for two arbitrary partial algebras, if their directed hypergraphs are isomorphic, then their weak, relative and strong subalgebra lattices are isomorphic. Secondly,...