nLab
E-infinity-ring

An $E_{\mathrm{\infty }}$-ring is a commutative monoid in the stable (∞,1)-category of spectra. Sometimes this is called a commutative ring spectrum. An E-∞ algebra in spectra.

This means that an $E_{\mathrm{\infty }}$-ring is an A-∞ ring that is commutative up to coherent higher homotopies.

Equivalently $E_{\mathrm{\infty }}$-rings may be modeled as ordinary commutative monoids with respect to the symmetric monoidal smash product of spectra.

$E_{\mathrm{\infty }}$-rings are the analoge in higher algebra of the commutative rings in ordinary algebra.