Free abelian group of countable rank

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Definition

This group, sometimes called the free abelian group of countable rank, is a free abelian group on a countably infinite generating set. Equivalently, it is the restricted external direct product of countably many copies of the group of integers.

It is to be contrasted with the Baer-Specker group, which is the unrestricted external direct product of countably many copies of the group of integers.