Ring of sets
From Wikipedia, the free encyclopedia
In mathematics, a nonempty collection of sets 
is called a ring (of sets) if it is closed under intersection and symmetric difference. That is, for any 
,
where 
represents the symmetric difference
A ring of sets forms an algebraic ring (possibly without unit) under these two operations. Intersection distributes over symmetric difference:
The empty set is the identity element for , and the union of all the sets, if it is in the ring, is the identity element for 
, making it a unit ring.
Given any set X, the power set of X forms a discrete ring of sets, while the collection {∅,X} constitutes the indiscrete ring of sets. Any field of sets and so also any σ-algebra also is a ring of sets.
