6 papers · 1 filter
Endomorphism rings of modules whose cardinality is cofinal to omega
Rüdiger Göbel, Saharon Shelah
The main result is Theorem: Let A be an R-algebra, mu, lambda be cardinals such that |A|<=mu=mu^{aleph_0}<lambda<=2^mu. If A is aleph_0-cotorsion-free or A is countably free, respe…
GCH implies the existence of many rigid almost free abelian groups
Rüdiger Göbel, Saharon Shelah
We begin with the existence of groups with trivial duals for cardinals aleph_n (n in omega). Then we derive results about strongly aleph_n-free abelian groups of cardinality aleph_…
Philip Hall's Problem On Non-Abelian Splitters
Rüdiger Göbel, Saharon Shelah
Philip Hall raised around 1965 the following question which is stated in the Kourovka Notebook: Is there a non-trivial group which is isomorphic with every proper extension of itse…
Localizations of Groups
Rüdiger Göbel, Saharon Shelah
A group homomorphism eta:A-> H is called a localization of A if every homomorphism phi:A-> H can be `extended uniquely' to a homomorphism Phi:H-> H in the sense that Phi eta = phi.…
On our paper `Almost Free Splitter', a correction
Rüdiger Göbel, Saharon Shelah
Let R be a subring of Q and recall from math.LO/9910161 that an R-module G is a splitter if Ext_R(G,G)=0. We correct the statement of Main Theorem 1.5 in math.LO/9910161. Assuming…
Reflexive subgroups of the Baer-Specker group and Martin's axiom
Rüdiger Göbel, Saharon Shelah
In two recent papers (math.LO/0003164 and math.LO/0003165) we answered a question raised in the book by Eklof and Mekler (p. 455, Problem 12) under the set theoretical hypothesis o…