A ring R is said to be left pure-hereditary (resp. RD-hereditary) if every left ideal of R is pure-
projective (resp. RD-projective). In this paper, some properties and examples of these rings …

We say that a ring R is a right RDV-ring if each simple right R-module is RD-injective. In this
paper, we study the notion of RDV-rings which is a non-trivial generalization of V-rings and …

We study direct-sum decompositions of pure-projective modules over some classes of rings.
In particular, we determine several classes of rings over which every pure-projective left …

A famous theorem of algebra due to Osofsky states that “if every cyclic left R-module is
injective, then R is semisimple”. Therefore, a natural question of this sort is:“What is the class …

A p-indigent module is one that is subprojective only to projective modules. An RD-
projective module is subprojective to any torsionfree (and flat) module. An RD-projective …

A left R-module M is said to be left singly injective if Ext R 1 (F/K, M)= 0 for any cyclic
submodule K of any finitely generated free left R-module F. In this paper, we study the notion …

A morphism f of left R-modules is called an RD-phantom morphism if the induced morphism
Tor1 (R= aR, f)= 0 for any a R. Similarly, a morphism g of left R-modules is said to be an …

In this paper, we study rings over which every simple right module is FC-pure flat. It is shown
that a normal right Artinian ring R with Jacobson radical J is a principal right ideal ring if and …

A ring R is called right pure-injective if it is injective with respect to pure exact sequences.
According to a well known result of L. Melkersson, every commutative Artinian ring is pure …

A classical question due to Yoneda is,“When is the tensor product of any two injective
modules injective?” Enochs and Jenda gave a complete and explicit answer to this question …