Splitting property of lattice ordered groups
States on unital partially-ordered groups
We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital -group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of...
Strong amalgamations of lattice ordered groups and modules.
Strongly projectable lattice ordered groups
Structure spaces of lattice ordered groups
Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group
The extension of a lattice ordered group by a generalized Boolean algebra will be denoted by . In this paper we apply subdirect decompositions of for dealing with a question proposed by Conrad and Darnel. Further, in the case when is linearly ordered we investigate (i) the completely subdirect decompositions of and those of , and (ii) the values of elements of and the radical .
Subdirect product decompositions of -algebras
Subdirect representation of tight Riesz groups by hybrid products.
Subdirectly irreducible MV-algebras
In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety.
Subgroups and hulls of Specker lattice-ordered groups
In this article, it will be shown that every -subgroup of a Specker -group has singular elements and that the class of -groups that are -subgroups of Specker -group form a torsion class. Methods of adjoining units and bases to Specker -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker -group.
Suprema of Classes of Generalized Scrimger Varieties of Lattice Ordered Groups.
Sur les endomorphismes conservant les polaires d'un groupe réticulé archimédien
Sur les homomorphismes d'hypergroupes
Sur les treillis de Coxeter finis
Björner (1984) a montré que l’ordre faible de Bruhat défini sur un groupe de Coxeter fini (Bourbaki 1969) est un treillis. Dans le cas du groupe symétrique ce résultat (treillis permutoèdre) a été prouvé par Guilbaud-Rosenstiehl (1963). Dans ce papier nous montrons que des propriétés connues des treillis permutoèdres peuvent s’étendre à tous les treillis de Coxeter finis et qu’inversement des propriétés démontrées sur tous les Coxeter finis ont des retombées intéressantes sur les permutoèdres....