Radical Integer

A radical integer is a number obtained by closing the Integers under Addition, Division, Multiplication, Subtraction, and Root extraction. An example of such a number is ${\root 3\of 7}+\sqrt{-2}-\sqrt{3+{\root 4\of 1+\sqrt{2}}}$ . The radical integers are a subring of the Algebraic Integers. If there are Algebraic Integers which are not radical integers, they must at least be cubic.