In stable homotopy theory, a ring spectrum is a spectrum E together with a multiplication map

1. μ: E E → E

and a unit map

1. η: S → E,

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,

1. μ (id μ) ~ μ (μ id)

and

1. μ (id η) ~ id ~ μ(η id).

Examples of ring spectra include singular homology with coefficients in a ring, complex cobordism, K-theory, and Morava K-theory.

See also

• Highly structured ring spectrum

References

de:Ringspektrum