Definition:Free Abelian Group on Set

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Definition

Let $\Z$ be the additive group of integers.

Let $S$ be a set.


The free abelian group on $S$ is the pair $(\Z^{(S)}, \iota)$ where:


Also denoted as

The free abelian group on $S$ is also denoted $\Z[S]$. Not to be confused with a polynomial ring.


Also see


Generalizations