"Although no other algebraic units are as famous as the golden ratio, they are of central importance to algebra."
Arguably more famous algebraic numbers include:
0, 1, The square root of two, the square root of any integer, i, any integer, the nth root of any integer,...
I realize that you were highlighting some specific, well-known examples, but I'm finding it pretty funny that you could have just said "the nth root of any integer", which encompasses all of the numbers and sets you mentioned before it. (I'm a maths student; it's finals; everything is hilarious now)
I only agree with your first three examples (the third being debatable). Square or higher roots of arbitrary integers are definitely less famous than the golden ratio though...
Arguably more famous algebraic numbers include: 0, 1, The square root of two, the square root of any integer, i, any integer, the nth root of any integer,...