Torsion-free abelian groups with prescribed finitely topologized endomorphism rings

Author:

Dugas Manfred,Göbel Rüdiger

Abstract

We will show that any complete Hausdorff ring R R which admits, as a basis of neighborhoods of 0, a family of right ideals I I with R / I R/I cotorsion-free can be realized as a topological endomorphism ring of some torsion-free abelian group with the finite topology. This theorem answers a question of A. L. S. Corner (1967) and can be used to provide examples in order to solve a problem (No. 72) in L. Fuchs’ book on abelian groups.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference19 articles.

1. Every countable reduced torsion-free ring is an endomorphism ring;Corner, A. L. S.;Proc. London Math. Soc. (3),1963

2. \bysame, Endomorphism rings of torsion-free abelian groups, Proc. Internat. Conf. on the Theory of Groups, Australian National University, Canberra, 1965, Gordon & Breach, New York, 1967, pp. 59-69.

3. \bysame, A topological ring with the property that every non-trivial idempotent is the infinite orthogonal sum of idempotents, Abelian Group Theory (Proc. Honolulu, 1983), Lecture Notes in Math., vol. 1006, Springer, Berlin and New York (to appear).

4. A theorem on the endomorphism ring of reduced torsion-free abelian groups and some applications;D’Este, Gabriella;Ann. Mat. Pura Appl. (4),1978

5. On topological rings which are endomorphism rings of reduced torsion-free abelian groups;D’Este, Gabriella;Quart. J. Math. Oxford Ser. (2),1981

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