claim does not seem correct

If $R$ is commutative, this is equivalent to being an integral domain.
But if R is the zero ring that it has no 1 != 0 so cannot be an
integral domain.
Maybe you want R is commutative with identity?

Parting words from the person who closed the correction:
In a few sources (but not many), an integral domain need not have a (nonzero) multiplicative identity. On the other hand, on PM, such rings are called cancellation rings. I will edit the object accordingly.
Status: Accepted
Reference to the user who closed the correction.:
Reference to the article this correction is about:
Status of the article (was it accepted?):
1
Status of the article (is it closed?):
1
What kind of correction is this:
Error