A **ring spectrum** is a concept from stable homotopy theory, which is a branch of algebraic topology. It generalizes the idea of a ring in the context of stable homotopy categories, allowing us to study constructions involving stable homotopy groups and cohomology theories in a coherent way. In more technical terms, a ring spectrum is a spectrum \( R \) that comes equipped with multiplication and unit maps that satisfy certain properties.
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A ring spectrum is a unital associative monoid object of the stable homotopy category under the smash product of spectra. It has and , satisfying the associative and two unit identities. Structured ring spectra additionally specify coherent point-set or higher homotopies; a ring object alone does not assert those enhancements.