Editing Universal coefficient theorem (section)

==Statement of the homology case ==
Consider the [[tensor product of modules]] <math>H_i(X,\Z)\otimes A</math>. The theorem states there is a [[short exact sequence]] involving the [[Tor functor]] 

:<math> 0 \to H_i(X, \Z)\otimes A \, \overset{\mu}\to \, H_i(X,A) \to \operatorname{Tor}_1(H_{i-1}(X, \Z),A)\to 0.</math>

Furthermore, this sequence [[splitting lemma|splits]], though not naturally. Here <math>\mu</math> is the map induced by the bilinear map <math>H_i(X,\Z)\times A\to H_i(X,A)</math>.
<!-- I'm pretty sure you mean that the homomorphism from the tensor product is induced by the bilinear map from the direct product.  Also, I am not sure how to embed latex in html but it looks like this works -->

If the coefficient ring <math>A</math> is <math>\Z/p\Z</math>, this is a special case of the [[Bockstein spectral sequence]].