symmetric monoidal (∞,1)-category of spectra
An -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 -ring is an A-∞ ring that is commutative up to coherent higher homotopies.
Equivalently -rings may be modeled as ordinary commutative monoids with respect to the symmetric monoidal smash product of spectra.
-rings are the analoge in higher algebra of the commutative rings in ordinary algebra.