# 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 -
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} }