{{Short description|Mathematical object}} {{one source |date=May 2024}} 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).<!-- Note this ''does not'' generalize Quillen's K-theory of a ring.;<ref>Warning 5 in http://www.math.harvard.edu/~lurie/281notes/Lecture20-Lower.pdf</ref> it is rather a generalization of a Waldhausen K-theory.-->
== See also == *G-spectrum
== References == {{Reflist}} *J. Lurie, [http://www.math.harvard.edu/~lurie/281notes/Lecture19-Rings.pdf Lecture 19: Algebraic K-theory of Ring Spectra]
Category:Spectra (topology)
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