Nonsingular prime rings containing a uniform left ideal and a uniform right ideal and the density theorem (Q1305235)

The author, after proving a series of lemmas in sections 1 and 2, proves the following main results. Let \(R\) be a left or right nonsingular prime ring containing a nonzero uniform left ideal and a nonzero uniform right ideal, the there is a division ring \(D\) and a \(D\)-vector space \(V\) such that \(R\) can be embedded in \(\text{Hom}_D(V,V)\) such that (i) \(R\) is a uniformly and essentially dense subring of \(\text{Hom}_D(V,V)\), (ii) \(Q_{\text{ms}}(R)\) is an essentially dense subring of \(\text{Hom}_D(V,V)\), (iii) \(Q_{\text{mr}}(R)=\text{Hom}_D(V,V)\). These results improve upon earlier results of Amitsur and Zelmanowitz. The author should have given more explanations by giving suitable references for the proofs of the subdivisions which are ommitted. This should have helped an average reader to read the paper without much difficulty.