if your axioms support multiplication you’ll get division out of them for free

this is true… except when it isn’t.

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist

https://en.wikipedia.org/wiki/Ring_(mathematics)

I like that they bring up all these informations, just to conclude, that neo-liberalism would be the solution (instead of the problem).