[Edit: I have completely changed the question in response to the replies given] 

I am curious if there is well defined notion of *reduced  $E_\infty$-ring*. 

Let $CAlg$ denote the $\infty$-category of $E_\infty$-ring, $CAlg_1$, the one category of communicative rings.  I would like to define the analog for *reduced ring*. 

One categorically,  $ CAlg_1^{red} \hookrightarrow CAlg_1$ admits a left adjoint $A \mapsto  A^{red}:=A /nil(A)$. 

--- 

We can define $$CAlg^{red} \hookrightarrow CAlg$$ as the $\infty$-cat. of $E_\infty$-rings whose underling  ring is reduced. 
Does there exist a left adjoint? As mentioned in comments by Marc, this is false. 

--- 

**Question[Edit]:** What *should* be the notion of  $E_\infty$-ring? Harry in the comment says that this should be an ordinary reduced ring. I would appreciate if some explanation could make this precise. 




  [1]: https://www.math.ias.edu/~lurie/papers/HA.pdf