# Conventions

The term “ring spectrum” refers to

*homotopy*ring spectrum.If $X$ is a

*based*space, we will denote $\Sigma ^\infty X$ by $X$ again. Thus, $E_*(X)$ is always reduced homology.If $X$ is an

*unbased*space, we will denote $\Sigma ^\infty _+ X$ by $X_+$. Thus, $E_*(X_+)$ is unreduced homology.