Titlebook: Ordered Algebraic Structures; Proceedings of the C Jorge Martinez Conference proceedings 1989 Kluwer Academic Publishers 1989 Abelian group

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Lattice-Ordered Groups of Divisibility: An Expository IntroductionThis paper discusses the interplay between the theories of abelian ℓ-groups and Bezout domains via the group of divisibility This interplay depends on a one-to-one correspondence between onto ℓ-homomorphisms and overrings. A method for interpreting ℓ-embeddings in the context of Bezout domains is conjectured.

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Recent Results on the Free Lattice-Ordered Group over a Right-Orderable GroupIn the following, we give a survey of recent results concerning when the free lattice-ordered group over a group retains some properties, such as nilpotency or solvability, of the original group.

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Periodic Extensions of Ordered GroupsA PARTIAL ORDER . on a group . is a subset . of . satisfying the following conditions:

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Some Applications of Definable Spine Analysis in Ordered Abelian GroupsThe quantifier elimination theorem for ordered abelian groups (o.a.g.) proved by Peter Schmitt [S], reduces the test for elementary equivalence of two ordered abelian groups G and H to countably many tests for elementary equivalence of Sp.(G) and Sp.(H) (definable spine) of convex subgroups of G and H.

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Representation of a real polynomial f(X) as a sum of 2m-th powers of rational functionsFrom Becker’s Satz 2.14 in [B.] it follows that a polynomial f ∈ ℝ[X] admits a representation .with g., h∈ ℝ[X] if and only if f satisfies the following three conditions:.Once f satisfies these conditions, the problem arises how to obtain a representation (1) for f. This paper is concerned with that problem.

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