Almost-free E-rings of cardinality aleph_1
| dc.creator | Göbel, Rüdiger | |
| dc.creator | Shelah, Saharon | |
| dc.creator | Strüngmann, Lutz | |
| dc.date | 2001-12-20 | |
| dc.date.accessioned | 2026-07-07T04:45:23Z | |
| dc.date.available | 2026-07-07T04:45:23Z | |
| dc.description | 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 <= lambda <= 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. | |
| dc.identifier | https://arxiv.org/abs/math/0112214 | |
| dc.identifier | http://arxiv.org/abs/math/0112214 | |
| dc.identifier | Canad. J. Math. 55 No. 4 (2003) 750--765 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62932 | |
| dc.subject | Logic | |
| dc.subject | Rings and Algebras | |
| dc.title | Almost-free E-rings of cardinality aleph_1 | |
| dc.type | text |