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Localization is considered a generalization because it introduces fraction-like elements into a general commutative ring, whereas the field of fractions construction only applies to integral domains. When $R$ is an integral domain and $S$ is chosen to be the set of nonzero elements, the localization $S^{-1}R$ recovers the familiar field of fractions.

Conditions: $R$ is a commutative ring.; In the special case, $R$ is an integral domain and $S$ is the set of nonzero elements of $R$.

Localization is considered a generalization because it introduces fraction-like elements into a general commutative ring, whereas the field of fractions construction only applies to integral domains. When $R$ is an integral domain and $S$ is chosen to be the set of nonzero elements, the localization $S^{-1}R$ recovers the familiar field of fractions.

Conditions: $R$ is a commutative ring.; In the special case, $R$ is an integral domain and $S$ is the set of nonzero elements of $R$.