# Regarding ideal of $\mathbb{N}$

Let $$\mathcal{I}$$ be an ideal of $$\mathbb{N}$$ i.e., if $$A\in \mathcal{I}$$ and $$B\subset A$$ then $$B \in \mathcal{I}$$ and if $$A, B \in \mathcal{I}$$ then $$A\cup B \in \mathcal{I}.$$ Then if $$\mathcal{I}$$ has the property that for any $$A\subset \mathbb{N}$$ and $$B\subset\mathbb{N}$$ either $$A\setminus B \in \mathcal{I}$$ or $$B\setminus A \in \mathcal{I}$$ then can anyone please suggest me that what type of ideal is this.