Definition:Ring of Sets/Definition 1

Definition
A ring of sets $\mathcal R$ is a non-empty system of sets such that for all $A, B \in \mathcal R$:
 * $(1): \quad A \cap B \in \mathcal R$
 * $(2): \quad A * B \in \mathcal R$

where $\cap$ denotes set intersection and $*$ denotes set symmetric difference.

That is, the operations $\cap$ and $*$ are closed in $\mathcal R$.

Also see

 * Equivalence of Definitions of Ring of Sets