In stable homotopy theory, a ring spectrum is a spectrum E together with a multiplication map and a unit map where S is the sphere spectrum.
These maps have to satisfy associativity and unitality conditions up to homotopy, much in the same way as the multiplication of a ring is associative and unital.
That is, and Examples of ring spectra include singular homology with coefficients in a ring, complex cobordism, K-theory, and Morava K-theory.
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