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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

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