RGB colours are a tuple of three hexadecimal numbers, $(r, g, b)$, where each entry satisfies $0\leq x \leq 15$. So addition is defined such that
$$ (r_1, g_1, b_1) + (r_2, g_2, b_2) = (\min(r_1+r_2, 15), \min(g_1+g_2, 15), \min(b_1+b_2, 15)) $$
because there is a limit to how red, green or blue something can be. Substraction is
$$ (r_1, g_1, b_1) - (r_2, g_2, b_2) = (\max(r_1-r_2, 0), \max(g_1-g_2, 0), \max(b_1-b_2, 0)) $$
This satisfies many of the axioms for a vector space (commutativity, associativity, identity element, etc.), with the exception of unique additive inverses. So it can't be a vector space, but it clearly shares many features. So what is this called? And how can its relationship to a vector space be described?
Looking at just the operation of addition, the set forms a commutative monoid, but this descriptions only covers the part where a regular vector space is also an Abelian group.
The closest I can find to describing the RGB structure is a monoid ring...