Displaying similar documents to “Simple and subdirectly irreducibles bounded distributive lattices with unary operators.”

On a certain construction of lattice expansions

Hector Gramaglia (2004)

Mathematica Bohemica


We obtain a simple construction for particular subclasses of several varieties of lattice expansions. The construction allows a unified approach to the characterization of the subdirectly irreducible algebras

A note on cylindric lattices

Ivo Düntsch (1993)

Banach Center Publications


0. Introduction. Besides being of intrinsic interest, cylindric (semi-) lattices arise naturally from the study of dependencies in relational databases; the polynomials on a cylindric semilattice are closely related to the queries obtainable from project-join mappings on a relational database (cf. [D] for references). This note is intended to initiate the study of these structures, and only a few, rather basic results will be given. Some problems at the end will hopefully stimulate further...

Closure Łukasiewicz algebras

Abad Manuel, Cimadamore Cecilia, Díaz Varela José, Rueda Laura, Suardíaz Ana (2005)

Open Mathematics


In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.

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

Leonardo Cabrer, Sergio Celani (2006)

Open Mathematics


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. ...

A note on Sugihara algebras.

Josep M. Font, Gonzalo Rodríguez Pérez (1992)

Publicacions Matemàtiques


In [4] Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it. In [3] it is stated that this quasivariety is the variety of Sugihara algebras. Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated...