Question

every field is a integral domain proof​

Answer 1

Answer:

Proof: Since a field is a commutative ring with unity, therefore, in order to show that every field is an integral domain we only need to prove that s field is without zero divisors. Let F be any field and let a,b∈F with a≠0 such that ab=0. Let 1 be the unity of F.

Step-by-step explanation:

Answer 2

Proof: Since a field is a causative ring with unity, therefore, in order to show thatevery field is an integral domain we only need to prove that s field is without zero divisors. Similarly if b≠0 then it can be shown that ab=0⇒a=0. ... Hence, a fieldis necessarily an integral domain.