A module UR is couniform if it has dual Goldie dimension 1, that is, it is non-zero and the
sum of any two proper submodules of UR is a proper submodule of UR. A module MR is …

In this paper we will first establish a duality between in jectivity and flatness for modules.
That is: Let E be a faithfully in jective module". Then, for each module A, we have W, dim. A …

A morphism f: M→ N of left R-modules is called a phantom morphism if the induced
morphism for every (finitely presented) right R-module A. Similarly, a morphism g: M→ N of …

Let R be an arbitrary ring and let (−)+= HomZ (−, Q/Z), where Z is the ring of integers and Q is
the ring of rational numbers. Let C be a subcategory of left R-modules and D a subcategory …

A module M is called dual-square-free (DSF) if M has no proper submodules A and B with
M= A+ B and M/A≅ M/B. The class of DSF-modules is closed under direct summands and …

For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

Let R be a left and right noetherian ring and M a finitely generated left Ä-module with Ext&
(Af, R)= 0 for i^ l. Is then M reflexive? This is a stronger version of the generalized Nakayama …

We characterize a ring over which every left module of finite length has an injective hull of
finite length. Using this, we show that finite normalizing extensions of such a ring also have …

We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …

In this note, we ask when the class of all finitely generated reflexive (torsionless) left
modules is closed under extensions. This is not always the case, even if R is left and right …