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Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is Ext R (G, G) = 0 holds and follow Schultz [22] to call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples for splitters. Are there others? Answering an open problem by Schultz [22] we will show that there are more… (More)

- Rüdiger Göbel, José L. Rodŕıguez, Saharon Shelah
- 2000

A group homomorphism η : H → G is called a localization of H if every Libman showed that a localization of a finite group need not be finite. This is exemplified by a well-known representation A n → SO n−1 (R) of the alternating group A n , which turns out to be a localization for n even and n ≥ 10. Emmanuel Farjoun asked if there is any upper bound in… (More)

Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is Ext R (G, G) = 0 holds. For simplicity we will call such modules splitters, see [16]. Also other names like stones are used, see a dictionary in Ringel's paper [14]. Our investigation continues [10]. In [10] we answered an open problem by constructing a large… (More)

- Rüdiger Göbel
- 1996

Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group Z ℵ 0 with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to Z. The Baer-Specker group, which is the additive group P = Z ℵ 0 of all integer-valued… (More)