I have shown specifically (with definitions), how the additive identity can be kept. As well as the distributive field axiom. I have shown how all field axioms remain unchanged. It is only a matter of changing the "properties" of numbers. Allow all numbers to be composed of numerical quantities, and dimensional unit quantities. You have but to give me the chance. For example...see the section "Distributive" in the thread "The Unified Number".
I would copy and paste, but "notation" is lost in translation. "Copy and paste" will not translate "underscores". Which is essential notation for the concept.
I appreciate your time, and intelligence. Especially knowing that I exasperate you.