Characterization of rings direct-projective modules direct-injective modules using and Page 1
Journal of Pure and Applied Algebra 87 (1993) 99-104 North-Holland 99 Characterization of …

Let R be a ring, and let n, d be non-negative integers. A right R-module M is called (n, d)-
projective if Ext d+ 1 R (M, A)= 0 for every n-copresented right R-module A. R is called right n …

In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

Let R be a ring with identity and M be a right unitary R-module. In this paper we introduce
the notion of strongly coretractable modules. Some basic properties of this class of modules …

One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition,
where a module M is called a C3-module if whenever A and B are direct summands of M …

Throughout this paper all rings will be associative with identity and modules will be unital
right modules. A ring R is called right CS-ring (or extending ring) if every right ideal I in R is …

A module satisfying the descending chain condition on cyclic submodules is called
coperfect. The class of coperfect modules lies properly between the class of locally artinian …

Abstract A module M is CS if every submodule of M is essential in a direct summand of M. In
this note we use the CS condition to provide conditions for semiperfect rings to be self …

A submodule N of a right R-module M is called coneat if for every simple right R-module S,
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …

We have defined aconcept of almost M-projectives and almost M-injectives in [4] and [9],
respectively. In the first section of this paper we give some relations among lifting modules …