Relations of Keune symbols (Q392600)

Let \(R\) be a unital associative ring with stable range one.NEWLINENEWLINEIn the case of a division ring \(D\) a theorem of \textit{U. Rehmann} [J. Reine Angew. Math. 301, 77--104 (1978; Zbl 0377.20036)] describes \(K_2(D)\) through a short exact sequence \(0\to K_2(D)\to U_D\to D^*\), where \(U_D\) is given by a presentation in terms of Steinberg symbols. Observe that for noncommutative \(D\) the Steinberg symols no longer describe elements of \(K_2(D)\). For our ring \(R\) of stable range one the Steinberg symbols need to be replaced by the more general Keune symbols. The authors describe a presentation for a group \(K_R\) that should play the role of \(U_D\) and announce that it fits in an exact sequence \(0\to K_2(R)\to K_R\to R^*\).