In algebra, a commutative k-algebra A is said to be 0-smooth if it satisfies the following lifting property: given a k-algebra C, an ideal N of C whose square is zero and a k-algebra map u : A → C / N {\displaystyle u:A\to C/N} , there exists a k-algebra map v : A → C {\displaystyle v:A\to C} such that u is v followed by the canonical map. If there exists at most one such lifting v, then A is said to be 0-unramified (or 0-neat).
In algebra, a commutative k-algebra A is said to be 0-smooth if it satisfies the following lifting property: given a k-algebra C, an ideal N of C whose square is zero and a k-algebra map u : A → C / N {\displaystyle u:A\to C/N} , there exists a k-algebra map v : A → C {\displaystyle v:A\to C} such that u is v followed by the canonical map. If there exists at most one such lifting v, then A is said to be 0-unramified (or 0-neat).
Source: Wikipedia "Smooth algebra" · CC BY-SA 4.0
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