User:Jshflynn/Kleene Plus is Semigroup

Theorem

Let $\Sigma$ be an alphabet.

Let $\Sigma^{+}$ be the Kleene plus of $\Sigma$ and $\circ$ denote concatenation.

Then $(\Sigma^{+}, \circ)$ is a semigroup.

Proof

Follows immediately from Kleene Plus is Linguistic Structure and Concatenation is Associative.

$\blacksquare$