Sh:773
- Shelah, S., & Strüngmann, L. H. (2002). Cotorsion theories cogenerated by \aleph_1-free abelian groups. Rocky Mountain J. Math., 32(4), 1617–1626. arXiv: math/0107208 DOI: 10.1216/rmjm/1181070044 MR: 1987629
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Abstract:
Given an \aleph_1-free abelian group G we characterize the class {\mathfrak C_G} of all torsion abelian groups T satisfying {\rm Ext}(G,T)=0 assuming the continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes {\mathfrak C}_G for arbitrary torsion-free abelian G. It follows that there exist some ugly \aleph_1-free abelian groups. - Version 2002-01-18_11 (7p) published version (10p)
Bib entry
@article{Sh:773,
author = {Shelah, Saharon and Str{\"u}ngmann, Lutz H.},
title = {{Cotorsion theories cogenerated by $\aleph_1$-free abelian groups}},
booktitle = {{Proceedings of the Second Honolulu Conference on Abelian Groups and Modules (Honolulu, HI, 2001)}},
journal = {Rocky Mountain J. Math.},
fjournal = {The Rocky Mountain Journal of Mathematics},
volume = {32},
number = {4},
year = {2002},
pages = {1617--1626},
issn = {0035-7596},
mrnumber = {1987629},
mrclass = {20K20 (20K15 20K35 20K40)},
doi = {10.1216/rmjm/1181070044},
note = {\href{https://arxiv.org/abs/math/0107208}{arXiv: math/0107208}},
arxiv_number = {math/0107208}
}