Algebraically compact group
In mathematics, in the realm of abelian group theory, a group is said to be algebraically compact if it is a direct summand of every abelian group containing it as a pure subgroup. Equivalent characterizations of algebraic compactness:
* The reduced part of the group is Hausdorff and complete in the adic topology.
* The group is pure injective, that is, injective with respect to exact sequences where the embedding is as a pure subgroup. Relations with other properties:
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Algebraically compact group
In mathematics, in the realm of abelian group theory, a group is said to be algebraically compact if it is a direct summand of every abelian group containing it as a pure subgroup. Equivalent characterizations of algebraic compactness:
* The reduced part of the group is Hausdorff and complete in the adic topology.
* The group is pure injective, that is, injective with respect to exact sequences where the embedding is as a pure subgroup. Relations with other properties:
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In mathematics, in the realm o ...... lations with other properties:
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Algebraically compact group
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