Ring spectrum

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.