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...

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 ⊂ ℝ m ( m ≥ 2 ) be an open set with a compact boundary B and let σ ≥ 0 be a finite measure on B . Consider the space L 1 ( σ ) of all σ -integrable functions on B and, for each f ∈ 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 ∈ 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 ∨ β exists in the partially ordered set Conv B . Further we show that each interval of Conv B is a Brouwerian lattice.

Σ -Hamiltonian and Σ -regular algebraic structures

Ivan Chajda, Petr Emanovský (1996)

Mathematica Bohemica

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The concept of a -closed subset was introduced in [1] for an algebraic structure = ( A , F , R ) of type and a set of open formulas of the first order language L ( ) . The set C ( ) of all -closed subsets of forms a complete lattice whose properties were investigated in [1] and [2]. An algebraic structure is called - hamiltonian, if every non-empty -closed subset of is a class (block) of some congruence on ; is called - regular, if = 𝔽 for every two , 𝔽 ∈ whenever they have a congruence class...

Nearly disjoint sequences in convergence l -groups

Ján Jakubík (2000)

Mathematica Bohemica

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For an abelian lattice ordered group G let G be the system of all compatible convergences on G ; this system is a meet semilattice but in general it fails to be a lattice. Let α n d be the convergence on G which is generated by the set of all nearly disjoint sequences in G , and let α be any element of G . In the present paper we prove that the join α n d ∨ α does exist in G .