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Displaying 741 – 760 of 1272

Orders of non-commutative rings. (Ordnungen nichtkommutativer Ringe.)

Hebisch, Udo, Lex, Wilfried (1990)

Séminaire Lotharingien de Combinatoire [electronic only]

Order-theoretic properties of some sets of quasi-measures

Zbigniew Lipecki (2017)

Commentationes Mathematicae Universitatis Carolinae

Let $𝔐$ and $ℜ$ be algebras of subsets of a set $Ω$ with $𝔐 \subset ℜ$ , and denote by $E (μ)$ the set of all quasi-measure extensions of a given quasi-measure $μ$ on $𝔐$ to $ℜ$ . We show that $E (μ)$ is order bounded if and only if it is contained in a principal ideal in $b a (ℜ)$ if and only if it is weakly compact and $extr E (μ)$ is contained in a principal ideal in $b a (ℜ)$ . We also establish some criteria for the coincidence of the ideals, in $b a (ℜ)$ , generated by $E (μ)$ and $extr E (μ)$ .

Ordres maximaux

Julien Querré (1964/1965)

Séminaire Dubreil. Algèbre et théorie des nombres

Orthogonal hull of a strongly projectable lattice ordered group

Ján Jakubík (1978)

Czechoslovak Mathematical Journal

Orthomodular lattices and closure operations in ordered vector spaces

Jan Florek (2010)

Banach Center Publications

On a non-trivial partially ordered real vector space (V,≤) the orthogonality relation is defined by incomparability and ζ(V,⊥) is a complete lattice of double orthoclosed sets. We say that A ⊆ V is an orthogonal set when for all a,b ∈ A with a ≠ b, we have a ⊥ b. In our earlier papers we defined an integrally open ordered vector space and two closure operations A → D(A) and $A \to A^{⊥ ⊥}$ . It was proved that V is integrally open iff $D (A) = A^{⊥ ⊥}$ for every orthogonal set A ⊆ V. In this paper we generalize this result. We...

Orthosymmetric bilinear map on Riesz spaces

Elmiloud Chil, Mohamed Mokaddem, Bourokba Hassen (2015)

Commentationes Mathematicae Universitatis Carolinae

Let $E$ be a Riesz space, $F$ a Hausdorff topological vector space (t.v.s.). We prove, under a certain separation condition, that any orthosymmetric bilinear map $T : E \times E \to F$ is automatically symmetric. This generalizes in certain way an earlier result by F. Ben Amor [On orthosymmetric bilinear maps, Positivity 14 (2010), 123–134]. As an application, we show that under a certain separation condition, any orthogonally additive homogeneous polynomial $P : E \to F$ is linearly represented. This fits in the type of results by...

$p$ -systems in local Noether lattices.

Johnson, E.W., Johnson, Johnny A., Taylor, Monty B. (1994)

International Journal of Mathematics and Mathematical Sciences

Pairs of partially ordered groups with the same convex subgroups

Milan Jasem (1987)

Mathematica Slovaca

Pairwise splitting lattice-ordered groups

Jorge Martinez (1977)

Czechoslovak Mathematical Journal

Partial dcpo’s and some applications

Zhao Dongsheng (2012)

Archivum Mathematicum

We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces $X$ , the corresponding partial dcpo’s of continuous real valued functions on $X$ are continuous partial dcpos; (iii) if a space $X$ is Hausdorff compact, the lattice of all S-lower semicontinuous functions on $X$ is the dcpo-completion of that of continuous real valued...