Full article: WHEN ARE PURE-INJECTIVE ENVELOPES OF FLAT MODULES FLAT? Skip
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If R is a right coherent ring, then left R-modules have covers by submodules of flat R-
modules if and only if all injective left R-modules have flat covers. This is the case if R is …

It is not known whether modules over an arbitrary ring have flat covers, however for certain
modules over commutative noetherian rings they can be shown to exist. These covers, in …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

The study-. of torsionfree covers started in the paper by Enochs 161 and continued in 111,
where the interesting result that any module over a integral domain has a torsionfree cover …

868 MARTINEZ HERNANDEZ where F'is a flat and F-divisible module, can be completed
commutatively. b) The diagram can be completed only by means of autornorphisms of F. In …

Throughout this paper all rings considered will be commutative rings with identity. We shall
consider the consequences for a ring of the flatness of certain classes of its modules. Since …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

An additive functor from the category of flat right R‐modules to the category of abelian
groups is continuous if it is isomorphic to a functor of the form−⊗ RM, where M is a left R …

1. Introduction. The notion of an injective cover has been recently introduced by Enochs r41
in terms of the dual of a categorical definition of an injective envelope. Earlier Enochs r31 …