5 papers
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…
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…
Some ugly aleph_1-free abelian groups
Saharon Shelah, Lutz Strüngmann
Given an aleph_1-free abelian group G we characterize the class C_G of all torsion abelian groups T satisfying Ext(G,T)=0 assuming the continuum hypothesis CH. Moreover, in Godel's…
It is consistent with ZFC that B_1-groups are not B_2-groups
Saharon Shelah, Lutz Strüngmann
A torsion-free abelian group B of arbitrary rank is called a B_1-group if Bext^1(B,T)=0 for every torsion abelian group T, where Bext^1 denotes the group of equivalence classes of…
The failure of the uncountable non-commutative Specker Phenomenon
Saharon Shelah, Lutz Strüngmann
Higman proved in 1952 that every free group is non-commutatively slender, this is to say that if G is a free group and h is a homomorphism from the countable complete free product…