An algebra of sets on a set 
is a collection 
of subsets of 
that contains 
and is closed under taking complements
in 
and finite unions (Hunter 2011, p. 56). It also contains the empty set and is closed under finite intersections and set
differences.
Every sigma-algebra is an algebra of sets, but an algebra of sets need not be closed under countable unions. The power set of 
and the collection 
are examples.
