👉 In mathematics, a subgrade (or "subgrain") is a subring of a ring. This means that it contains all but one element of the original ring. For example, in the ring of integers $\mathbb{Z}$, the subrings are $\mathbb{Z}/n\mathbb{Z}$ for $n > 1$. The set of all subgrains is denoted as $\text{Subgrains}(\mathbb{Z})