>operator inversion identities like a−(b+c)=(a−b)−ca−(b+c)=(a−b)−c, a−(b−c)=(a−b)+ca−(b−c)=(a−b)+c, and their multiplicative analogues. I don't know names for these algebraic laws either.

Isn't that the distributive property of multiplication over addition? There is a -1 that gets multiplied.