Cotorsion group

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

In abelian group theory, an abelian group is said to be cotorsion if every extension of it by a torsion-free group splits. If the group is , this says that for all torsion-free groups . It suffices to check the condition for the group of rational numbers.

More generally, a module M over a ring R is said to be a cotorsion module if Ext1(F,M)=0 for all flat modules F. This is equivalent to the definition for abelian groups (considered as modules over the ring Z of integers) because over Z flat modules are the same as torsion-free modules.

Some properties of cotorsion groups:

External links[edit]

  • Fuchs, L. (2001) [1994], "Cotorsion group", in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4