Question

Prove that every field is an integral domain

Answer 1

Answer:

Step-by-step explanation:let F be a field, we have to show that it is an integral domain for this (we need to prove) their is only to show (F,+,•) is without zero divisor.

Answer 2

An integral domain is a nontrivial finite commutative ring with no divisor of zero.

If a and b are field elements with ab = 0, then if a is not equal to  0 has an inverse a-1, combining all these sides by this produces b = 0. As a result, there are no zero-divisors, and we get: Every domain is a part of the whole. An integral domain is a field. A field is a finite integral domain.