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Projectability and weak homogeneity of pseudo effect algebras

Ján Jakubík (2009)

Czechoslovak Mathematical Journal

In this paper we deal with a pseudo effect algebra 𝒜 possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, 𝒜 can be represented as an interval of a unital partially ordered group G . We prove that 𝒜 is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of 𝒜 and of G is shown to be valid.

Riesz spaces of order bounded disjointness preserving operators

Fethi Ben Amor (2007)

Commentationes Mathematicae Universitatis Carolinae

Let L , M be Archimedean Riesz spaces and ℒ b ( L , M ) be the ordered vector space of all order bounded operators from L into M . We define a Lamperti Riesz subspace of ℒ b ( L , M ) to be an ordered vector subspace ℒ of ℒ b ( L , M ) such that the elements of ℒ preserve disjointness and any pair of operators in ℒ has a supremum in ℒ b ( L , M ) that belongs to ℒ . It turns out that the lattice operations in any Lamperti Riesz subspace ℒ of ℒ b ( L , M ) are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem for Riesz homomorphisms....

Rigid extensions of ℓ -groups of continuous functions

Michelle L. Knox, Warren Wm. McGovern (2008)

Czechoslovak Mathematical Journal

Let C ( X , ℤ ) , C ( X , ℚ ) and C ( X ) denote the ℓ -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space X , respectively. Characterizations are given for the extensions C ( X , ℤ ) ≤ C ( X , ℚ ) ≤ C ( X ) to be rigid, major, and dense.

Sequential convergences on free lattice ordered groups

Ján Jakubík (1992)

Mathematica Bohemica

In this paper the partially ordered set Conv G of all sequential convergences on G is investigated, where G is either a free lattice ordered group or a free abelian lattice ordered group.

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