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 א0 is undecidable in ZFC. While they exist in Gödel's universe, they do not exist in other models of set theory. For a regular cardinal א1 ≤ λ ≤ 2א0 we construct E-rings of cardinality λ in ZFC which have א1 -free additive structure. For λ = א1 we therefore obtain the existence of almost-free E-rings of cardinality א1 in ZFC.
Original language | English |
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Pages (from-to) | 750-765 |
Number of pages | 16 |
Journal | Canadian Journal of Mathematics |
Volume | 55 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2003 |
Keywords
- Almost-free modules
- E-rings