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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.

S V -Rings and S V -Porings

Niels Schwartz (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

S V -rings are commutative rings whose factor rings modulo prime ideals are valuation rings. S V -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of S V -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered S V -rings ( S V -porings) are introduced, and...

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