On relative enumerability of Turing degrees

Let d be a Turing degree, R[d] and Q[d] denote respectively classes of recursively enumerable (r.e.) and all degrees in which d is relatively enumerable. We proved in [ta] that there is a degree d containing differences of r.e.sets (briefly, d.r.e.degree) such that R[d] possess a least element m>0. Now we show the existence of a d.r.e. d such that R[d] has no a least element. We prove also that for any REAdegree d below 0′ the class Q[d] cannot have a least element and more generally is not bounded below by a non-zero degree, except in trivial