Direct product decompositions of infinitely distributive lattices

Ján Jakubík

Displaying similar documents to “Direct product decompositions of infinitely distributive lattices”

$Σ$ -isomorphic algebraic structures

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

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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...

Atomicity of the Boolean algebra of direct factors of a directed set

Ján Jakubík (1998)

Mathematica Bohemica

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In the present paper we deal with the relations between direct product decompositions of a directed set $L$ and direct product decompositions of intervals of $L$ .

Essential norms of a potential theoretic boundary integral operator in $L^{1}$

Josef Král, Dagmar Medková (1998)

Mathematica Bohemica

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Let $G \subset ℝ^{m}$ $(m \geq 2)$ be an open set with a compact boundary $B$ and let $σ \geq 0$ be a finite measure on $B$ . Consider the space $L^{1} (σ)$ of all $σ$ -integrable functions on $B$ and, for each $f \in L^{1} (σ)$ , denote by $f σ$ the signed measure on $B$ arising by multiplying $σ$ by $f$ in the usual way. $𝒩_{σ} f$ denotes the weak normal derivative (w.r. to $G$ ) of the Newtonian (in case $m > 2$ ) or the logarithmic (in case $n = 2$ ) potential of $f σ$ , correspondingly. Sharp geometric estimates are obtained for the essential norms of the operator $𝒩_{σ} - α I$ (here $α \in ℝ$ ...

Disjoint sequences in Boolean algebras

Ján Jakubík (1998)

Mathematica Bohemica

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We deal with the system $Conv B$ of all sequential convergences on a Boolean algebra $B$ . We prove that if $α$ is a sequential convergence on $B$ which is generated by a set of disjoint sequences and if $β$ is any element of $Conv B$ , then the join $α \lor β$ exists in the partially ordered set $Conv B$ . Further we show that each interval of $Conv B$ is a Brouwerian lattice.

Displaying similar documents to “Direct product decompositions of infinitely distributive lattices”

Σ -isomorphic algebraic structures

Atomicity of the Boolean algebra of direct factors of a directed set

Essential norms of a potential theoretic boundary integral operator in L 1

Disjoint sequences in Boolean algebras

$Σ$ -isomorphic algebraic structures

Essential norms of a potential theoretic boundary integral operator in $L^{1}$