A structure theorem for abelian quasi-ordered groups

The Hahn Embedding Theorem for Abelian Lattice-ordered Groups

The Structure Theorem for Finitely Generated Abelian Groups

This paper provides a thorough explication of the Structure Theorem for Abelian groups and of the background information necessary to prove it. The outline of this paper is as follows. We first consider some theorems related to abelian groups and to R-modules. In this section we see that every finitely generated abelian group is the epimorphic image of a finitely generated free abelian group. H...

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...

Characterizing automorphism groups of ordered abelian groups

In this short note we want to characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of abelian groups, see [2]. Recall that H is a right ordered group (RO-group) if (H, ·) is a group and (H,<) is a linear order satisfying...

A Simple Proof of the Marker-steinhorn Theorem for Expansions of Ordered Abelian Groups

We give a short and self-contained proof of the MarkerSteinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.