The difference between Field of fractions and Integral domain
When used as nouns, field of fractions means the smallest field in which a given ring can be embedded, whereas integral domain means any nonzero commutative ring in which the product of nonzero elements is nonzero.
check bellow for the other definitions of Field of fractions and Integral domain
-
Field of fractions as a noun (algebra, ring theory):
The smallest field in which a given ring can be embedded.
-
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]]."