Bockstein factorization through integral cohomology
= Bockstein factorization through integral cohomology
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{title2=$\beta=\rho\widehat\beta$}
The <Bockstein homomorphism> for $0\to\mathbb Z/n\to\mathbb Z/n^2\to\mathbb Z/n\to0$, with injection $[a]\mapsto[na]$, is coefficient reduction $\rho$ after the <integral Bockstein homomorphism>. The commuting maps of coefficient sequences prove this by naturality of the <connecting homomorphism>.