UMP for Free Modules
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UMP for free modules
Let \(R\) be a ring, \(M\) a free \(R\)-module with basis \(B\), \(N\) an \(R\)-module, \(j:B\to N\) a function. Then there exists a unique \(R\)-module homomorphism \(h:M\to N\) such that \(h(b)=j(b)\ \forall b\in B\).
As \(m=\sum_{i=1}^n r_ib_i,\ b_i\in B\) unique, imples \(h(m):=\sum_{i=1}^n r_ij(b_i)\) is well defined
