symmetric monoidal (∞,1)-category of spectra
For $R$ a commutative ring, its nilradical $I \subset R$ is the ideal of nilpotent elements: the collection of those elements $a \in R$ such that there is $n \in \mathbb{N}$ with $a^n = 0$.
The quotient $R/I$ is also called the reduced part of $R$.
(If $R$ is not commutative there are different generalization of the notion of nilradical. See wikipedia, for the moment.)
With rings regarded as formal duals of affine schemes, the canonical inclusion
is to be thought of as exhibiting the inclusion of $Spec R/I$ into an infinitesimal thickening of itself.
For $X : CRing \to Set$ a presheaf on the category of commutative rings, the presheaf
is called the de Rham space of $X$.