The difference between Commutative ring and Integral domain
When used as nouns, commutative ring means a ring whose multiplicative operation is commutative, whereas integral domain means any nonzero commutative ring in which the product of nonzero elements is nonzero.
check bellow for the other definitions of Commutative ring and Integral domain
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Commutative ring as a noun (algebra, ring theory):
A ring whose multiplicative operation is commutative.
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Integral domain as a noun (algebra, ring theory):
Any nonzero commutative ring in which the product of nonzero elements is nonzero.
Examples:
"A ring <math>R</math> is an integral domain if and only if the polynomial ring <math>R[x]</math> is an integral domain."
"For any integral domain there can be derived an associated [[field of fractions]]."