Question

Give an example of integral domain that is not a field.

Answer 1

sorry i had not studied it yet but u can prefer this

http://en.wikipedia.org/wiki/Integral_domain

Answer 2

A field satisfies the field axioms. You have two options: (1) find an integral domain and modify it to violate a field axiom or (2) find an integral domain that does not satisfy the field axioms.

The field axioms are here: http://en.wikipedia.org/wiki/Field_(mathematics)#Definition_and_illustration

Answer 3

Basically, the one thing that fields have that integral domains do not is closure under inverses for the multiplication. The easiest example of this is Z. Z is clearly an integral domain: it's a commutative ring, there are no zero divisors, and it's non-trivial. Z is not closed under inverses for the multiplication, though, so it is not a field.

Answer 4

ok..thank you guys.. =)

Answer 5

You're welcome.