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Cotorsion-free algebras as endomorphism algebras in L - the discrete and topological cases

Rüdiger E. Göbel, Brendan Goldsmith (1993)

Commentationes Mathematicae Universitatis Carolinae

The discrete algebras A over a commutative ring R which can be realized as the full endomorphism algebra of a torsion-free R -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, V = L . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...

Dense pairs of o-minimal structures

Lou van den Dries (1998)

Fundamenta Mathematicae

The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of "small definable set" plays a special role in this description.

Elementary embeddings in torsion-free hyperbolic groups

Chloé Perin (2011)

Annales scientifiques de l'École Normale Supérieure

We describe first-order logic elementary embeddings in a torsion-free hyperbolic group in terms of Sela’s hyperbolic towers. Thus, if H embeds elementarily in a torsion free hyperbolic group Γ , we show that the group Γ can be obtained by successive amalgamations of groups of surfaces with boundary to a free product of  H with some free group and groups of closed surfaces. This gives as a corollary that an elementary subgroup of a finitely generated free group is a free factor. We also consider the...

Endomorphisms of symbolic algebraic varieties

Misha Gromov (1999)

Journal of the European Mathematical Society

The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...

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