nLab
dg-ideal

A dg-ideal $J\subset A$ is an alternative name for an ideal in a dg-algebra $A$, i.e. a $A$-$A$-dg-subbimodule of $A$. Of course, one can also talk about one-sided ideals.

This means that $J$ is a graded sub-vector space that is closed under product by element in $A$ from either side, and closed under acting with the differential.