# nLab nonunital Ek-algebra

### Context

#### Higher algebra

higher algebra

universal algebra

# Contents

## Idea

The nonunital variant of Ek-algebra, hence the generalization of the concept of nonunital ring from algebra to higher algebra.

## Properties

### Relation to augmented $\mathbb{E}_k$-algebra

Nonunital $\mathbb{E}_k$-algebras are equivalent to unital $\mathbb{E}_k$-algebras sliced over the free $\mathbb{E}_k$-algebra on a single generator.

In particular nonunital E-∞ algebras are equivalent to unital $E_\infty$-algebras sliced over the sphere spectrum:

$E_\infty Ring^{nu} \simeq E_\infty Ring_{/\mathbb{S}} \,,$

where the map from right to left is given by $\mathbb{E}_k$-unitalization and the converse by forming augmentation ideals.

## References

Last revised on August 22, 2014 at 07:09:05. See the history of this page for a list of all contributions to it.