Free Abelian paratopological groups over metric spaces

Lindelöf Σ-Spaces and R-Factorizable Paratopological Groups

We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally ω-narrow and satisfies celω(G) ≤ ω, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group.

Intuitionistic Free Abelian Groups

Divisibility Properties of Group Rings over Torsion-free Abelian Groups

Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...

CoGalois groups as metric spaces

The coGalois group associated to a torsion free cover of a Z-module are known to have a canonical topology. In this paper we will see that this topology can be deduced by p-roots of elements of coGalois groups over Zp (p is a prime). We shall investigate in the metric associated to this topology and deduce that the coGalois groups are complete and are isomorphic as metric spaces to products of ...

Free abelian lattice-ordered groups

Let n be a positive integer and FA`(n) be the free abelian latticeordered group on n generators. We prove that FA`(m) and FA`(n) do not satisfy the same first-order sentences in the language L={+,−, 0,∧,∨} if m 6= n. We also show that Th(FA`(n)) is decidable iff n ∈ {1, 2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. A. M. S. C...