The field is called an algebraic closure of if is algebraic over and if every polynomial splits completely over , so that can be said to contain all the elements that are algebraic over .
For example, the field of complex numbers is the algebraic closure of the field of reals.
is called an algebraic closure of 
if 
is algebraic over 
and if every polynomial 
splits completely over 
, so that 
can be said to contain all the elements that are algebraic over 
. 
is the algebraic closure of the field of reals 
.