Question

prove ZOZ is not an integral domain.​

Answer 1

Answer:

Integral domains and Fields

These are two special kinds of ring

Definition

If a, b are two ring elements with a, b ≠ 0 but ab = 0 then a and b are called zero-divisors.

Example

In the ring Z6 we have 2.3 = 0 and so 2 and 3 are zero-divisors.

More generally, if n is not prime then Zn contains zero-divisors.

Definition

An integral domain is a commutative ring with an identity (1 ≠ 0) with no zero-divisors.

That is ab = 0 ⇒ a = 0 or b = 0.