Definition:Sigma-Ring/Definition 1

Definition
A $\sigma$-ring is a ring of sets which is closed under countable unions.

That is, a ring of sets $\Sigma$ is a $\sigma$-ring :
 * $\ds A_1, A_2, \ldots \in \Sigma \implies \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma$

Also see

 * Equivalence of Definitions of Sigma-Ring