On Utumi's Ring of Quotients

Abstract

The purpose of this note is to establish and exploit the fact that Utumi's maximal ring of right quotients (6) of an associative ring R (let us say with 1) is the bicommutator of the minimal injective extension of R regarded as a right R-module. Nothing new will be said about Johnson's ring of quotients (4), which is still the most important case.