0

In this question, $\bigoplus_{\mathbb N} \mathbb Z$ is given as an example of a group that is freely generated but not finitely generated. A similar question is asked here but it has been closed because it does not provide the context in which the operator is used.

Shaun
  • 44,997
Poseidaan
  • 551
  • 6
    Direct sum. As a set it consists of sequences $(z_n)_{n\in\Bbb{N}}$ such that $z_n\in\Bbb{Z}$ for all $n$, and only finitely many of them are non-zero. The latter condition marks the difference between a direct sum and a direct product. The group operation is that of $\Bbb{Z}$, i.e. addition, done componentwise. – Jyrki Lahtonen Nov 22 '21 at 10:51
  • 2
    Notation (perhaps confusing?):$$\bigoplus_{\mathbb N} \mathbb Z = \mathbb Z\oplus \mathbb Z\oplus \mathbb Z\oplus \mathbb Z\oplus\cdots$$ where there the copies of $\mathbb Z$ are indexed by $\mathbb N$. – GEdgar Nov 22 '21 at 11:58
  • See this post for more details. – Dietrich Burde Nov 22 '21 at 13:53

0 Answers0