Let \(R\) be a ring and \(M\) a left $R$-module. A subset \(B\subseteq M\) is a basis of \(M\) if \(B\) is linearly independent and a generating set for \(M\).
An \(R\)-module is free exactly when it has a basis.
Basis of a module
D-I7D56
D-I7D56
Let \(R\) be a ring and \(M\) a left $R$-module. A subset \(B\subseteq M\) is a basis of \(M\) if \(B\) is linearly independent and a generating set for \(M\).
An \(R\)-module is free exactly when it has a basis.