The field axioms are generally written in additive and multiplicative pairs. name | addition | multiplication associativity | (a + b) + c = a + (b + c) | (a b) c = a(b c) commutativity | a + b = b + a | a b = b a distributivity | a(b + c) = a b + a c | (a + b) c = a c + b c identity | a + 0 = a = 0 + a | a·1 = a = 1·a inverses | a + (-a) = 0 = (-a) + a | a a^(-1) = 1 = a^(-1) a if a!=0

algebra | field