Commutative ring spectrum

In algebraic topology, a commutative ring spectrum, roughly equivalent to a $E_{\infty }$-ring spectrum, is a commutative monoid in a good category of spectra. For example, a sphere spectrum is a commutative ring spectrum.

See also: Highly structured ring spectrum and derived scheme.

Almost all reasonable categories of commutative ring spectra can be shown to be Quillen equivalent to each other. Thus, from the point view of the stable homotopy theory, the term "commutative ring spectrum" may be used as a synonymous to a $E_{\infty }$-ring spectrum.

References

• J.P. May, What precisely are $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra? arXiv:0903.2813