Decomposability of low 2-computably enumerable degrees and Turing jumps in the Ershov hierarchy

In this paper we prove the following theorem: For every notation of constructive ordinal, there exists a low 2-computably enumerable degree which is not splittable into two lower 2-computably enumerable degrees, whose jumps belong to the $\Delta$-level of the Ersov hierarchy that corresponds to this notation.