Corrigendum: A completion for partially ordered abelian groups.
Covering condition in the lattice of radical classes of linearly ordered groups
Decomposition of group-valued measures on orthoalgebras
We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the case where the measure is order bounded instead of being positive. This last result generalizes A. D. Aleksandrov's...
Dedekind extension of measures with values in vector lattices.
Dense pairs of o-minimal structures
The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of "small definable set" plays a special role in this description.
Directoid groups
We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.
Distinguished extensions of an -algebra
Distributivität des -Untergruppenverbandes einer Verbandsgruppe
Distributivity in lattice ordered groups
DRl-semigroups and -algebras
Egoroff, σ, and convergence properties in some archimedean vector lattices
An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each there are and a ∈ A with λₙaₙ ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC ⇒ RUC): if aₙ ↓ 0 then aₙ → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the form D(X) (all extended real continuous functions on the compact space X) showing that (σ) and (OC ⇒ RUC) are equivalent, and equivalent...
Eindeutigkeit des Darstellungsraumes von Vektorverbänden.
Embeddings of totally ordered MV-algebras of bounded cardinality
For a given cardinal number 𝔞, we construct a totally ordered MV-algebra M(𝔞) having the property that every totally ordered MV-algebra of cardinality at most 𝔞 embeds into M(𝔞). In case 𝔞 = ℵ₀, the algebra M(𝔞) is the first known MV-algebra with respect to which the deductive system for the infinitely-valued Łukasiewicz's propositional logic is strongly complete.
Embeddings of Valued Groups.
Epi-archimedean groups
Extensions of dimension groups and AF C*-algebras.
Extensions of positive operators and extreme points. I
Extensions of positive operators and extreme points. II
Extensions of positive operators and extreme points. III
Extensions of positive operators and extreme points. IV