A combinatorial principle and endomorphism rings I: On p-groups

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Two lines of research are involved here. One is a combinatorial principle, proved in ZFC for many cardinals (e.g., any λ = λא 0) enabling us to prove things which have been proven using the diamond or for strong limit cardinals of uncountable cofinality. The other direction is building abelian groups with few endomorphisms and/or prescribed rings of endomorphisms. We prove that for a ring R, whose additive group is the p-adic completion of a free p-adic module, R is isomorphic to the endomorphism ring of some separable abelian p-group G divided by the ideal of small endomorphisms, with G of power λ for any λ = λא 0≧|R|.

Original languageEnglish
Pages (from-to)239-257
Number of pages19
JournalIsrael Journal of Mathematics
Volume49
Issue number1-3
DOIs
StatePublished - Sep 1984

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