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.
• 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 $\aleph_1$}},
journal = {Canad. J. Math.},
fjournal = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques},
volume = {55},
number = {4},
year = {2003},
pages = {750--765},
issn = {0008-414X},
doi = {10.4153/CJM-2003-032-8},
mrclass = {20K20 (13F10 20K30)},
mrnumber = {1994072},
mrreviewer = {A. Mader},
doi = {10.4153/CJM-2003-032-8},
note = {\href{https://arxiv.org/abs/math/0112214}{arXiv: math/0112214}},
arxiv_number = {math/0112214}
}