# nLab E-infinity-ring

### Context

#### Higher algebra

higher algebra

universal algebra

## Theorems

#### Stable Homotopy theory

stable homotopy theory

# Contents

An ${E}_{\infty }$-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 ${E}_{\infty }$-ring is an A-∞ ring that is commutative up to coherent higher homotopies.

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

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

Revised on July 20, 2012 15:20:50 by Stephan Alexander Spahn (79.219.126.169)