Divisibility orders on semigroups. II.
Divisible effect algebras and interval effect algebras
It is shown that divisible effect algebras are in one-to-one correspondence with unit intervals in partially ordered rational vector spaces.
Divisor class groups of ordered subgroups
Domain representability of
Let be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) is Scott-domain representable; (b) is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal T₁-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk that is...
Domain-representable spaces
We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if X is domain-representable, then so is any -subspace of X. It follows that any Čech-complete...
Domination properties in ordered Banach algebras
We recall from [9] the definition and properties of an algebra cone C of a real or complex Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A. The Banach algebra A is then called an ordered Banach algebra. An important property that the algebra cone C may have is that of normality. If C is normal, then the order structure and the topology of A are reconciled in a certain way. Ordered Banach algebras have interesting spectral properties....
Doubt fuzzy BCI-algebras.
DRl-semigroups and -algebras
Dual commutative hyper K-ideals of type 1 in hyper K-algebras of order 3.
In this note we classify the bounded hyper K-algebras of order 3, which have D1 = {1}, D2 = {1,2} and D3 = {0,1} as a dual commutative hyper K-ideal of type 1. In this regard we show that there are such non-isomorphic bounded hyper K-algebras.
Dual spaces of totally ordered rings
Dualität zwischen Kategorien topologischer Räume und Kategorien von K-Verbänden.
Dualities for Stone algebras, double Stone algebras, and relative Stone algebras
Dually residuated -monoids having no non-trivial convex subalgebras
In this note we describe the structure of dually residuated -monoids (-monoids) that have no non-trivial convex subalgebras.
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.
Einschließung inverser Elemente durch Fixpunktverfahren.
Embeddings into Power Series Rings.
Embeddings into Simple Lattice-ordered Groups with Different First Order Theories.
Embeddings of chains into chains
Continuity of isotone mappings and embeddings of a chain G into another chain are studied. Especially, conditions are found under which the set of points of discontinuity of such a mapping is dense in G.
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.