# Module spectrum

In algebra, a **module spectrum** is a spectrum with an action of a ring spectrum; it generalizes a module in abstract algebra.

The ∞-category of (say right) module spectra is stable; hence, it can be considered as either analog or generalization of the derived category of modules over a ring.

## K-theory

Lurie defines the K-theory of a ring spectrum *R* to be the K-theory of the ∞-category of perfect modules over *R* (a perfect module being defined as a compact object in the ∞-category of module spectra.)

## See also

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