Right orders and amalgamation for lattice-ordered groups

Autor: A. M. W. Glass, V. V. Bludov
Rok vydání: 2011
Předmět:
Zdroj: Mathematica Slovaca. 61:355-372
ISSN: 1337-2211
0139-9918
DOI: 10.2478/s12175-011-0017-2
Popis: Let H i be a sublattice subgroup of a lattice-ordered group G i (i = 1, 2). Suppose that H 1 and H 2 are isomorphic as lattice-ordered groups, say by φ. In general, there is no lattice-ordered group in which G 1 and G 2 can be embedded (as lattice-ordered groups) so that the embeddings agree on the images of H 1 and H 1φ. In this article we prove that the group free product of G 1 and G 2 amalgamating H 1 and H 1φ is right orderable and so embeddable (as a group) in a lattice-orderable group. To obtain this, we use our necessary and sufficient conditions for the free product of right-ordered groups with amalgamated subgroup to be right orderable [BLUDOV, V. V.—GLASS, A. M. W.: Word problems, embeddings, and free products of right-ordered groups with amalgamated subgroup, Proc. London Math. Soc. (3) 99 (2009), 585–608]. We also provide new limiting examples to show that amalgamation can fail in the category of lattice-ordered groups even when the amalgamating sublattice subgroups are convex and normal (ℓ-ideals) and solve of Problem 1.42 from [KOPYTOV, V. M.—MEDVEDEV, N. YA.: Ordered groups. In: Selected Problems in Algebra. Collection of Works Dedicated to the Memory of N. Ya. Medvedev, Altaii State University, Barnaul, 2007, pp. 15–112 (Russian)].
Databáze: OpenAIRE
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