# Closure of Recognizable Languages under Kleene Star: Algebraic Proof?

Let $Rec(\Sigma)$ be the class of languages over $\Sigma^*$ recognizable by finite monoids.

To show that $Rec(\Sigma)$ is closed under Kleene star, one would usually refer to the equivalence of recognizable and regular languages and invoke Kleene's theorem. Can anyone think of a direct algebraic proof of this closure property on the level of monoids?