Steenrod algebra

In algebraic topology, a Steenrod algebra was defined by Henri Cartan (1955) to be the algebra of stable cohomology operations for mod ${\displaystyle p}$ cohomology.

For a given prime number ${\displaystyle p}$, the Steenrod algebra ${\displaystyle A_{p}}$ is the graded Hopf algebra over the field ${\displaystyle \mathbb {F} _{p}}$ of order ${\displaystyle p}$, consisting of all stable cohomology operations for mod ${\displaystyle p}$ cohomology. It is generated by the Steenrod squares introduced by Norman Steenrod (1947) for ${\displaystyle p=2}$, and by the Steenrod reduced ${\displaystyle p}$th powers introduced in Steenrod (1953a, 1953b) and the Bockstein homomorphism for ${\displaystyle p>2}$.

The term "Steenrod algebra" is also sometimes used for the algebra of cohomology operations of a generalized cohomology theory.