Statement:
Every Abelian group has a divisible hull. (If \(A\) and \(B\) are groups, \(B\) is a divisible hull of \(A\) means \(B\) is a divisible group, \(A\) is a subgroup of \(B\) and for every non-zero \(b \in B\), \(\exists n \in \omega \) such that \(0\neq nb\in A\).) Fuchs [1970], Theorem 24.4 p 107.
Howard_Rubin_Number: 180
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Hodges-1980: Constructing pure injective hulls
Book references
Infinite Abelian groups I, Fuchs, L., 1970
Note connections:
Note 24
This note contains some definitions from group
theory that are used in \(\cal M22\), and forms [62 C], [62 D], [67 D], Form 180, and Form 308\((p)\)