# Sh:785

• Göbel, R., Shelah, S., & Strüngmann, L. H. (2003). Almost-free E-rings of cardinality \aleph_1. Canad. J. Math., 55(4), 750–765.
• Abstract:
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 cardinality greater than 2^{\aleph_0} is undecidable in ZFC. While they exist in Goedel’s universe, they do not exist in other models of set theory. For a regular cardinal \aleph_1\leq\lambda\leq 2^{\aleph_0} we construct E-rings of cardinality \lambda in ZFC which have \aleph_1-free additive structure. For \lambda= \aleph_1 we therefore obtain the existence of almost-free E-rings of cardinality \aleph_1 in ZFC.
• Version 2002-01-18_11 (17p) published version (16p)
Bib entry
@article{Sh:785,
author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon and Str{\"u}ngmann, Lutz H.},
title = {{Almost-free $E$-rings of cardinality $\aleph_1$}},
}