Cotorsion group

In mathematics, in the realm of 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 $M$ , this is equivalent to asserting that $Ext(F,M) = 0$ for all torsion-free groups $F$ . It suffices to check the condition for $F$ being the group of rational numbers.

单词	Cotorsion
释义	Cotorsion 英语百科 Cotorsion group In mathematics, in the realm of 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 $M$ , this is equivalent to asserting that $Ext(F,M) = 0$ for all torsion-free groups $F$ . It suffices to check the condition for $F$ being the group of rational numbers.
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