Free commutative skew braces

The main result of this paper is an explicit construction of the free commutative skew brace – that is, a skew brace whose circle group is commutative – on an arbitrary generating set $X$. We embed this object into a set of rational functions and show that a simple linear equation characterizes the image of this embedding. As a consequence, comparing elements in this skew brace is no more difficult than comparing elements in the free commutative group generated by $X$.