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 language | English |
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Pages (from-to) | 239-257 |
Number of pages | 19 |
Journal | Israel Journal of Mathematics |
Volume | 49 |
Issue number | 1-3 |
DOIs | |
State | Published - Sep 1984 |