Huh. Didn’t think that a field needed to have division defined on it, at least not in the ‘multiplication is the opposite of division’ way you’d expect. Learn something new every day.

actually I dont think it does. A field has addition and multiplication as operations.

To get subtraction you have a negative element for each element in the field (such that a + (-a) = 0). similarly there is an inverse of every element exept 0 (a * 1/a = 1)

but then it might aswell be like defining 4 operations so thats maybe a better way to think about it