… projective. This follows from the fact that every free module can be embedded in a projective
injective module… is injective. Compare this to the definition of Quasi Frobenius ring [5]:''Every …

… M denotes a fixed jβ-module. We first recall the notions of M-projective and ilf-injective modules
… out that ϋMnjective modules are the same as the injective modules over R. However ϋJ-…

… -injective module. It is known that if R is left Artinian, then it is left Noetherian and has only a
finite number of simple ϋί-modules… are indecomposable quasi-injective modules and that this …

… In this case we have exactly one indecomposable projective-injective module, namely
the projective cover Pšw0Ž of the unique simple standard (or Verma) module in this block. …

… , d)-injective right R-module N. After giving some basic properties of (n, d)-projective modules
and (n, d)-injective modules, we … 𝒫 n, d ) denotes the class of all (n, d)-injective (resp. (n, d)-…

… N-injective and weakly injective modules are … injective right A-module is weakly projective.
We also study those rings over which every weakly projective right module is weakly injective. …

… quasi-projective modules to be injective and ones for quasi-injective modules to be projective.
In [ … Now we induce the property of the indecomposable quasi-projective injective module. …

… Locally injective and locally projective modules have further interesting properties which
we also present here. … Therefore, tt(Q) is the injective module we were looking for …

… E( ) denotes the injective envelope. In section 4 we study the annihilator relations between
the ring R and an i?-injective module. Our faithfully injective modules are characterized in fact …

… rings whose injective modules are R-projective (respectively, max-projective) are characterized.
For a commutative Noetherian ring R, we prove that injective modules are R-projective if …