So my Logic teacher gave us this exercise:
Define a monomorphism between these 2 models/language structures or prove that it is impossible to define: $$a) \left<\Bbb N , \leq, +, 0\right> \& \left<\Bbb N , \leq, \cdot, 1\right>$$ $$b) \left<\Bbb N , \cdot, 1\right> \& \left<\Bbb N , +, 0\right>$$
I believe there is none for a), but yes for b) because the order relation $\leq$ won't allow it, but no matter what I imagine, nothing works.
Does anybody have any idea? Thank you beforehand :)