Isn’t this expression $E^+.E^+ = E^+$ wrong?

Let $\sum = {a, b}$ then $E^+$ will have ‘a’ & ‘b’ as the smallest string but $E^+.E^+$ will have ‘aa’, ‘ab’, ‘ba’ & ‘bb’ as its smallest string. There will not be any string of length 1.

So, $E^+.E^+ \neq E^+$.