Noncommutative rings whose modules have essential flat envelopes (Q1903025)

A flat envelope has been defined by replacing injective by flat in the normal definition of an injective hull. It is not known over which rings every left module has a flat envelope. This paper does not answer this question, but makes some progress in that direction by characterizing (for noncommutative rings) those IF-rings \(R\) for which every left \(R\)- module has an essential flat envelope. The paper concludes with a section containing a number of examples showing the not very nice behaviour of monomorphic flat envelopes, as well as questions raised by the examples.