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Natural extension of a congruence of a lattice to its lattice of convex sublattices

S. Parameshwara Bhatta, H. S. Ramananda (2011)

Archivum Mathematicum

Let L be a lattice. In this paper, corresponding to a given congruence relation Θ of L , a congruence relation Ψ Θ on C S ( L ) is defined and it is proved that 1. C S ( L / Θ ) is isomorphic to C S ( L ) / Ψ Θ ; 2. L / Θ and C S ( L ) / Ψ Θ are in the same equational class; 3. if Θ is representable in L , then so is Ψ Θ in C S ( L ) .

Normalization of basic algebras

Miroslav Kolařík (2008)

Discussiones Mathematicae - General Algebra and Applications

We consider algebras determined by all normal identities of basic algebras. For such algebras, we present a representation based on a q-lattice, i.e., the normalization of a lattice.

Note on algebraic interior systems

Ivan Chajda (2005)

Discussiones Mathematicae - General Algebra and Applications

We get an interrelation between an algebraic closure system and its conjugated interior system. We introduce the concept of algebraic interior system and we get its representation.

Note on "construction of uninorms on bounded lattices"

Xiu-Juan Hua, Hua-Peng Zhang, Yao Ouyang (2021)

Kybernetika

In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.

Note on dense covers in the category of locales

Jan Paseka (1994)

Commentationes Mathematicae Universitatis Carolinae

In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.

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