= Bockstein cohomology
{c}
{title2=$H\beta^q(X;n)=\ker\beta_q/\operatorname{im}\beta_{q-1}$}
The degree-one <Bockstein homomorphism> makes modulo-$n$ <cohomology> into a <cochain complex>. Its cohomology is the Bockstein cohomology. For prime $n$ this is a graded vector space; for composite $n$ it is a graded $\mathbb Z/n$-module. For $\mathbb{RP}^3$ at modulus two, its only nonzero groups are $\mathbb F_2$ in degrees zero and three. This is the cohomological counterpart of <Bockstein homology>.
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