Universal property of a free module
= Universal property of a free module
A module $F$ is free on a set $S$ exactly when every function from $S$ to any module $N$ extends uniquely to an $R$-module homomorphism $F\to N$.
= Universal property of a free module
A module $F$ is free on a set $S$ exactly when every function from $S$ to any module $N$ extends uniquely to an $R$-module homomorphism $F\to N$.