The axiomatic rank of the quasivariety of orderable groups is infinite.
The Cauchy extension of an ordered abelian group realized by -valuations
The Galois connection between weak torsion and sub-product classes of -groups
The -Classes of Archimedean -groups with Weak Unit
denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar and from universal algebra are here meant in . and denote the integers and the reals, with unit 1, qua-objects. denotes a non-void finite set of positive integers. Let be non-void and not . We show(1), and(2) if and only if Our proofs are, for the most part, simple calculations. There is no real use of methods of universal algebra (e.g., free objects), and only one restricted...
The ideal and new interval topologies on l-groups
The Interval Topology of an -Group
The lattice of solid -subgroups of a retractable group
The lattice of topologies of topological -groups
The partial-isometric crossed products of by the forward and backward shifts.
The Redfield topology on some groups of continuous functions.
The Redfield topology on the space of real-valued continuous functions on a topological space is studied (we call it R-topology for short). The R-neighbourhoods are described relating them to the connectedness for the carriers. The main results are: If the space is totally disconnected without isolated points, the R-topology is not discrete. Under suitable conditions on the space, R-convergence implies pointwise or uniform convergence. Under some restrictions, R-convergence for a net implies that...
The semigroup of varieties of weakly associative lattice groups
The structure of a complete -group
The structure of transitive ordered permutation groups
We give some necessary and sufficient conditions for transitive -permutation groups to be -transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive -permutation groups to be normal-valued.
The theory of quasi-divisors on cartesian products
The -completion of a lattice ordered group
Topological automorphism groups of chains.
It is shown that any set-open topology on the automorphism group A(X) of a chain X coincides with the pointwise topology and that A(X) is a topological group with respect to this topology. Topological properties of connectedness and compactness in A(X) are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.
Topological characterizations of ordered groups with quasi-divisor theory
For an order embedding of a partly ordered group into an -group a topology is introduced on which is defined by a family of valuations on . Some density properties of sets , and ( being -ideals in ) in the topological space are then investigated, each of them being equivalent to the statement that is a strong theory of quasi-divisors.
Topologies corresponding to metrics on -groups
Topologies in -groups
Topology on regulators of lattice ordered groups. I. Topology induced by an -group