Steenrod algebra

Summary

The mod $2$ Steenrod algebra $\mathcal{A}_2$ is the graded algebra over $\Z/2\Z$ generated by the Steenrod squares, subject to the Adem relations. It is the algebra of all stable cohomology operations on mod $2$ cohomology. So the mod $2$ cohomology of every space is a module over it. For each odd prime $p$ there is an analogous algebra built from the reduced powers and the Bockstein. The Steenrod algebra is a Hopf algebra, and it is the input of the Adams spectral sequence, which computes stable homotopy groups.