-posets
Darstellungen und Erweiterungen geordneter Mengen. I.
Darstellungen und Erweiterungen geordneter Mengen. II.
Das Assoziativgesetz als Kummutativitätsaxiom in Boole'schen Zwerchverbänden.
Decomposition of commutative ordered semigroups into archimedean components.
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...
Decomposition of -group-valued measures
We deal with decomposition theorems for modular measures defined on a D-lattice with values in a Dedekind complete -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for -group-valued...
Decomposition of regular subsemigroup lattices.
Decomposition of topologies on lattices and hyperspaces [Book]
Décompositions d'une fonction de plusieurs variables
Decompositions in lattices and some representations of algebras [Book]
Decompositions of directed sets with zero
Decompositions of semigroups with zero.
Dedekind completions of lattices by ends
Dedekind cuts in C(X)
The aim of this paper is to show that every Hausdorff continuous interval-valued function on a completely regular topological space X corresponds to a Dedekind cut in C(X) and conversely.
Dedekind extension of measures with values in vector lattices.
Deductive systems of BCK-algebras
In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator of a deductive system is the the pseudocomplement of . These results are more general than that the similar results given by M. Kondo in [7].
Definition of Flat Poset and Existence Theorems for Recursive Call
This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this...
Definitions of finiteness based on order properties
A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Choice (AC) is assumed, is equivalent to stating that the set is finite; several such definitions have been studied over the years. In this article we introduce a framework for generating definitions of finiteness in a systematical way: basic definitions are obtained from properties of certain classes of binary relations, and further definitions are obtained from the basic ones by closing them under subsets...