# Sh:721

• Göbel, R., Shelah, S., & Wallutis, S. L. (2001). On the lattice of cotorsion theories. J. Algebra, 238(1), 292–313.
• Abstract:
We discuss the lattice of cotorsion theories for abelian groups. First we show that the sublattice of the well–studied rational cotorsion theories can be identified with the well–known lattice of types. Using a recently developed method for making Ext vanish we also prove that any power set together with the ordinary set inclusion (and thus any poset) can be embedded into the lattice of all cotorsion theories.
• Current version: 2001-02-12_10 (19p) published version (22p)
Bib entry
@article{Sh:721,
author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon and Wallutis, Simone L.},
title = {{On the lattice of cotorsion theories}},
journal = {J. Algebra},
fjournal = {Journal of Algebra},
volume = {238},
number = {1},
year = {2001},
pages = {292--313},
issn = {0021-8693},
mrnumber = {1822193},
mrclass = {20K35 (16E30)},
doi = {10.1006/jabr.2000.8619},
note = {\href{https://arxiv.org/abs/math/0103154}{arXiv: math/0103154}},
arxiv_number = {math/0103154}
}