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...
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].
Demi-groupes 0-simples et complètement 0-simples totalement ordonnés. Application aux demi-groupes de matrices de Rees
Demi-groupes et catégories à involution
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.
Die Verbände mit nichteinfacher Funktionenalgebra.
Dimension in algebraic frames
In an algebraic frame the dimension, , is defined, as in classical ideal theory, to be the maximum of the lengths of chains of primes , if such a maximum exists, and otherwise. A notion of “dominance” is then defined among the compact elements of , which affords one a primefree way to compute dimension. Various subordinate dimensions are considered on a number of frame quotients of , including the frames and of -elements and -elements, respectively. The more concrete illustrations...
Direct decompositions of dually residuated lattice-ordered monoids
The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.
Direct factors of directed groups
Direct factors of multilattice groups
Direct factors of multilattice groups. II.
Subgroups of a directed distributive multilattice group are characterized which are direct factors of . The main result is formulated in Theorem 2.
Direct limits of cyclically ordered groups
Direct product decomposition of -algebras
Direct product decompositions of bounded commutative residuated -monoids
The notion of bounded commutative residuated -monoid (-monoid, in short) generalizes both the notions of -algebra and of -algebra. Let be a -monoid; we denote by the underlying lattice of . In the present paper we show that each direct...
Direct product decompositions of directed groups
Direct product decompositions of pseudo effect algebras
Direct product factors in GMV-algebras