Rings which have flat injective modules

Coflat rings and modules

“…Colby has proved in [4] the analogous result for FC rings and locally finite groups (i.e., groups in which every finite subset generates a finite subgroup). THEOREM …”

“…Since the ^-Baer criterion is simply the restriction of the general Baer criterion (i.e., The Injective Test Lemma (see [2,Lemma 18.3])) to finitely generated right ideals, Colby [4] 2. («=>) This proof parallels 1 completely and thus will be omitted.…”

“…In this section we focus on a class of rings, called FC rings, that generalize the class of QF rings. These rings are a slight variation of a class of rings first introduced by Colby [4] In spite of this last fact, the class of FC rings, with their built in left-right symmetry, displays many properties analogous to those of the smaller class of QF rings. Before stating some of them we recall a few things.…”

Finite homomorphic images of Bezout duo-domains

“…Finally, in [2] it is proved that a Bezout ring R is a right and left IF-ring if and only if it is coherent and P-injective. By [3,10] we know that every IF-ring either has zero weak global dimension or it is infinite.…”

“…The necessity is straightforward as this is a property of each von Neumann regular ring, and the sufficiency follows from the observation that R/aR is an IF-ring (by the Theorem 13) of zero weak global dimension [2].…”