The field axioms are generally written in additive or multiplicative pairs. $$ \begin{array}{|c|c|c|} \hline \text{Name} & \text{Addition} & \text{Multiplication} \\ \hline \text{Associativity} & (a + b) + c = a + (b + c) & (ab)c = a(bc) \\ \hline \text{Commutativity} & a+b=b+a & ab = ba \\ \hline \text{Distributivity} & a(b+c) = ab + ac & (a+b)c = ac + bc \\ \hline \text{Identity} & a+0=a=0+a & a \cdot 1 = a = 1 \cdot a \\ \hline \text{Inverse} & a + (-a) = 0 = (-a) + a & a a^{-1} = 1 = a^{-1} a \text{ for } a \neq 0\\ \hline \end{array} $$