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Field Axioms

The field axioms are generally written in additive and multiplicative pairs.

nameadditionmultiplication
associativity(a+b)+c=a+(b+c)(ab)c=a(bc)
commutativitya+b=b+aab=ba
distributivitya(b+c)=ab+ac(a+b)c=ac+bc
identitya+0=a=0+aa·1=a=1·a
inversesa+(-a)=0=(-a)+aaa^(-1)=1=a^(-1)a if a!=0

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