… section 3 we define a co-semisimple module as one relative to which every simple module
is injective. It turns out that these modules are just those whose homomorphisms into simple …

… if and only if every simple module over ,4 is injective. A ring A … if’ every simple left (respectively
right) A -module is injective. … modules considerc53 blr, us are unitary left modules. For any …

… In view of the injective envelope-like properties of E, It is unfortunate that we must use the
injective envelope. However, the author sees no way to remove this difficulty at the present time…

… V -ring if simple right R-modules are injective. … simple module is either injective or projective.
Right GV-rings were introduced in [9]. A module M is called quasi-injective if it is M-injective. …

… We characterize when every X-module is M-injective in this … every simple &-module being
M-injective implies that every 3-… is a V-module if and only if every simple module is M-injective. …

… Generalizations of injectivity have been discussed in many papers, for example, see Citation…
(m, n)-injective modules are defined and studied. We prove that M R is (m, n)-injective if and …

… rings whose simple modules are all injective, called V-rings. In this paper, we consider rings
over which every simple module is either injective or furthest from being injective, in some …

… finitely many isomorphism classes of indecomposable injective left R-modules then there is
a finitely presented left module T which is a test module for both injectivity and flatness. (d) If …

… simple p-poor modules. In fact, it is shown (in Theorem 2.10) that the simple R-module R / m
… We prove that for an ideal a of R the simple module R / m is R / a -injective if and only if a ⊈ …

… Now we study the conditions of injectivity of simple FG-modules. Let R be a ring and A be
a simple R-module, and put E =EndR(A). If φ ∈EndR(A), then Ker φ and Im φ are R-…