Vector lattices over subfields of the reals

Bixler, Patrick; Conrad, Paul; Powell, Wayne B.; Tsinakis, Constantine

doi:10.1017/s1446788700029918

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…The reader is cautioned from the start that this is different from the coproduct in the category of all abelian -groups, which is discussed in [M73a] and [BCPT90]. The spirit of the results is in keeping with those in the latter reference, however.…”

Section: Ftcs Of Archimedean -Groups: Reductionsmentioning

confidence: 80%

New torsion theory in unital abelian ℓ-groups

Martínez

2011

Mathematica Slovaca

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ABSTRACT. This paper introduces the notion of a functorial torsion class (FTC): in a concrete category C which has image factorization, one considers monocoreflective subcategories which are closed under formation of subobjects.Here the interest is in FTCs in the category of abelian lattice-ordered groups with designated strong order unit. The FTCs T consisting of archimedean latticeordered groups are characterized: for each subgroup A of the rationals with the identity 1, either T = S(A), the class of all lattice-ordered groups of functions on a set X which have finite range in A, or T = T(A), the class of all subgroups of A with 1.As for FTCs possessing non-archimedean groups, it is shown that if T is an FTC containing a subgroup A of the reals with 1, of rank two or greater, then T contains all -groups of the form A → × G, for all abelian lattice-ordered groups G. Finally, the least FTC that contains a non-archimedean group is the class of all Z → × G, for all abelian lattice-ordered groups G.

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Section: Ftcs Of Archimedean -Groups: Reductionsmentioning

confidence: 80%

New torsion theory in unital abelian ℓ-groups

Martínez

2011

Mathematica Slovaca

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Torsion Classes of Vector Lattices

Conrad

Lin

Nelson

1993

Ordered Algebraic Structures

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On the Riesz structures of a lattice ordered abelian group

Lenzi

2019

Mathematica Slovaca

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A Riesz structure on a lattice ordered abelian group G is a real vector space structure where the product of a positive element of G and a positive real is positive. In this paper we show that for every cardinal k there is a totally ordered abelian group with at least k Riesz structures, all of them isomorphic. Moreover two Riesz structures on the same totally ordered group are partially isomorphic in the sense of model theory. Further, as a main result, we build two nonisomorphic Riesz structures on the same l-group with strong unit. This gives a solution to a problem posed by Conrad in 1975. Finally we apply the main result to MV-algebras and Riesz MV-algebras.

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Vector lattices over subfields of the reals

Cited by 3 publications

References 13 publications

New torsion theory in unital abelian ℓ-groups

New torsion theory in unital abelian ℓ-groups

Torsion Classes of Vector Lattices

On the Riesz structures of a lattice ordered abelian group

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