Almost-free E-rings of cardinality א1

Rüdiger Göbel*, Saharon Shelah, Lutz Strüngmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish
Pages (from-to)750-765
Number of pages16
JournalCanadian Journal of Mathematics
Volume55
Issue number4
DOIs
StatePublished - Aug 2003

Keywords

  • Almost-free modules
  • E-rings

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