For all scalars \(\{a, b, c\} \subseteq F\), it

• commutes, so

  \(a + b = b + a\)

• associates, so

  \((a + b) + c = a + (b + c)\),

• has the exactly one additive identity: \(0\), so

  \(a + 0 = a\),

• has the exactly one additive inverse: \(-a\), so

  \(a + (-a) = 0\).