8 papers · 1 filter
Generalized E-Rings
Rüdiger Göbel, Saharon Shelah, Lutz Strüngmann
A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End(R_Z) of the additive group R_Z, taking any r in R to the endomorphism left multiplica…
Uniquely Transitive Torsion-free Abelian Groups
Rüdiger Göbel, Saharon Shelah
We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a uniqu…
On universal and epi-universal locally nilpotent groups
Rüdiger Göbel, Saharon Shelah, Simone Wallutis
In this paper we mainly consider the class LN of all locally nilpotent groups. We first show that there is no universal group in LN_lambda if lambda is a cardinal such that lambda…
Almost-free E-rings of cardinality aleph_1
Rüdiger Göbel, Saharon Shelah, Lutz Strüngmann
An E-ring is a unital ring R such that every endomorphism of the underlying abelian group R^+ is multiplication by some ring-element. The existence of almost-free E-rings of cardin…
On the existence of rigid aleph_1-free abelian groups of cardinality aleph_1
Rüdiger Göbel, Saharon Shelah
An abelian group is said to be aleph_1-free if all its countable subgroups are free. Our main result is: If R is a ring with R^+ free and |R|<lambda <= 2^{aleph_0}, then there exis…
On the lattice of cotorsion theories
Rüdiger Göbel, Saharon Shelah, Simone Wallutis
We discuss the lattice of cotorsion theories for abelian groups. First we show that the sublattice of the well-studied rational cotorsion theories can be identified with the well-k…