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Lattice effect algebras densely embeddable into complete ones

Zdena Riečanová (2011)

Kybernetika

An effect algebraic partial binary operation ø p l u s defined on the underlying set E uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion E ^ of E there exists an effect algebraic partial binary operation ^ then ^ need not be an extension of . Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for that ^ existing on E ^ is an extension of defined on E . Further we show that such ^ extending exists at most...

Lattices of relative colour-families and antivarieties

Aleksandr Kravchenko (2007)

Discussiones Mathematicae - General Algebra and Applications

We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices...

Lattices of Scott-closed sets

Weng Kin Ho, Dong Sheng Zhao (2009)

Commentationes Mathematicae Universitatis Carolinae

A dcpo P is continuous if and only if the lattice C ( P ) of all Scott-closed subsets of P is completely distributive. However, in the case where P is a non-continuous dcpo, little is known about the order structure of C ( P ) . In this paper, we study the order-theoretic properties of C ( P ) for general dcpo’s P . The main results are: (i) every C ( P ) is C-continuous; (ii) a complete lattice L is isomorphic to C ( P ) for a complete semilattice P if and only if L is weak-stably C-algebraic; (iii) for any two complete semilattices...

Lexicographic extensions of dually residuated lattice ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Mathematica Bohemica

Dually residuated lattice ordered monoids ( D R -monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ( M V -algebras, B L -algebras) and their non-commutative variants ( G M V -algebras, pseudo B L -algebras). In the paper, lex-extensions and lex-ideals of D R -monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.

Local bounded commutative residuated -monoids

Jiří Rachůnek, Dana Šalounová (2007)

Czechoslovak Mathematical Journal

Bounded commutative residuated lattice ordered monoids ( R -monoids) are a common generalization of, e.g., B L -algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative R -monoids are investigated.

Localic Katětov-Tong insertion theorem and localic Tietze extension theorem

Yong Min Li, Wang Guo-jun (1997)

Commentationes Mathematicae Universitatis Carolinae

In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.

Locally functionally countable subalgebra of ( L )

M. Elyasi, A. A. Estaji, M. Robat Sarpoushi (2020)

Archivum Mathematicum

Let L c ( X ) = { f C ( X ) : C f ¯ = X } , where C f is the union of all open subsets U X such that | f ( U ) | 0 . In this paper, we present a pointfree topology version of L c ( X ) , named c ( L ) . We observe that c ( L ) enjoys most of the important properties shared by ( L ) and c ( L ) , where c ( L ) is the pointfree version of all continuous functions of C ( X ) with countable image. The interrelation between ( L ) , c ( L ) , and c ( L ) is examined. We show that L c ( X ) c ( 𝔒 ( X ) ) for any space X . Frames L for which c ( L ) = ( L ) are characterized.

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