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Displaying 1 – 20 of 97

$𝒵$ -distributive function lattices

Marcel Erné (2013)

Mathematica Bohemica

It is known that for a nonempty topological space $X$ and a nonsingleton complete lattice $Y$ endowed with the Scott topology, the partially ordered set $[X, Y]$ of all continuous functions from $X$ into $Y$ is a continuous lattice if and only if both $Y$ and the open set lattice $𝒪 X$ are continuous lattices. This result extends to certain classes of $𝒵$ -distributive lattices, where $𝒵$ is a subset system replacing the system $𝒟$ of all directed subsets (for which the $𝒟$ -distributive complete lattices are just the continuous...

2-normalization of lattices

Ivan Chajda, W. Cheng, S. L. Wismath (2008)

Czechoslovak Mathematical Journal

Let $τ$ be a type of algebras. A valuation of terms of type $τ$ is a function $v$ assigning to each term $t$ of type $τ$ a value $v (t) \geq 0$ . For $k \geq 1$ , an identity $s \approx t$ of type $τ$ is said to be $k$ -normal (with respect to valuation $v$ ) if either $s = t$ or both $s$ and $t$ have value $\geq k$ . Taking $k = 1$ with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called $k$ -normal (with respect to the valuation $v$ ) if all its identities are $k$ -normal. For any variety $V$ , there is a least...

$ℓ$ -многообразия без независимого базиса тождеств. II.

N.Ya. Medvedev (1985)

Mathematica Slovaca

Łukasiewicz tribes are absolutely sequentially closed bold algebras

Roman Frič (2002)

Czechoslovak Mathematical Journal

We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean $M V$ -algebra) can be uniquely extended to a sequentially continuous measure on the generated Łukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on Łukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields...

$𝔪$ -poproduct of lattices

Zuzana Ladzianska (1985)

Mathematica Slovaca

$δ$ -ideals in pseudo-complemented distributive lattices

M. Sambasiva Rao (2012)

Archivum Mathematicum

The concept of $δ$ -ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of $δ$ -ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of $δ$ -ideals. Finally, some properties of $δ$ -ideals are studied with respect to homomorphisms and filter congruences.

$λ$ -lattices

Václav Snášel (1997)

Mathematica Bohemica

In this paper, we generalize the notion of supremum and infimum in a poset.

$ϱ$ -ideals in the lattice of semi $ϱ$ -ideals

Jaromír Duda (1981)

Archivum Mathematicum

$σ$ -elements in multiplicative lattices

C. Jayaram, E. W. Johnson (1998)

Czechoslovak Mathematical Journal

$Σ$ -isomorphic algebraic structures

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

For an algebraic structure $= (A, F, R)$ or type and a set $Σ$ of open formulas of the first order language $L ()$ we introduce the concept of $Σ$ -closed subsets of . The set $ℂ_{Σ} ()$ of all $Σ$ -closed subsets forms a complete lattice. Algebraic structures , of type are called $Σ$ -isomorphic if $ℂ_{Σ} () ≅ ℂ_{Σ} ()$ . Examples of such $Σ$ -closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study $Σ$ -isomorphic algebraic structures in dependence on the...