Steenrod algebra is a fundamental concept in algebraic topology, specifically in the study of cohomology theories. It arises from the work of the mathematician Norman Steenrod in the mid-20th century and is primarily concerned with the operations on the cohomology groups of topological spaces. The core idea behind Steenrod algebra is the introduction of certain cohomology operations, known as Steenrod squares, which act on the cohomology groups of topological spaces.
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The Steenrod algebra organizes stable mod- cohomology operations. At it is generated by the Steenrod squares; at an odd prime it is generated by the Steenrod reduced powers and Bockstein homomorphism. Cohomology is a module over this algebra, and every continuous map induces a homomorphism preserving its action.