Noncancellable, singular, and conjugate degrees

We study degree structures of stronger algorithmic reducibilities inside the degrees of weaker algorithmic ones. Results in this area are reviewed for algorithmic reducibilities $m$-, $1$-, $tt$-, $wtt$-, $T$-, $e$-, $s$-, $Q$-, and we formulate questions that are still not settled for these. A computably enumerable $Q$-degree which consists of one computably enumerable $m$-degree is constructed.