What are field axioms?

Answer 1

Field Axioms are assumed truths regarding a collection of items in a field.

Let a, b, c be elements of a field F. Then:

Commutativity:

a+b=b+a and a*b=b*a

Associativity:

(a+b)+c=a+(b+c) and (a*b)*c = a*(b*c)

Distributivity:

a*(b+c)=a*b+b*c

Existence of Neutral Elements:

There exists a zero element 0 and identify element i, such that,

a+0=a

a*i=a

Existence of Inverses:

There is an element -a such that,

a+(-a)=0

for each a unequal to the zero element, there exists an a' such that

a*a'=1