Rings and Modules of Quotients

Abstract

The development of a general theory of rings of quotients may be said to have started with the construction by Johnson [1] of the maximal ring of quotients Qmax of a non-singular ring A. This was done before the theory of injective envelopes had become available, but it was later proved that Qmax could be used as an injective envelope of the ring A. The maximal ring of quotients of an arbitrary ring A was defined by Utumi [1] and studied by Findlay and Lambek [1]. In particular, Lambek [2] proved that it could be interpreted as the bicommutator of the injective envelope of A.