We introduce the notion of t-Rickart modules as a generalization of t-Baer modules. Dual t-
Rickart modules are also defined. Both of these are generalizations of continuous modules …

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 …

Let R be a ring. A right R-module A is said to be C-flat if the kernel of any epimorphism B→ A
is C-pure in B, ie the induced map Hom (C, B)→ Hom (C, A) is surjective for any cyclic right …

Recall that a left module A (resp. right module B) is said to be singly injective (resp. singly
flat) if Ext^ 1 _ R (F/K, A)= 0 E xt R 1 (F/K, A)= 0 (resp. Tor _ 1^ R (B, F/K)= 0 Tor 1 R (B, F/K) …

R is said to be a right AFG ring if the right annihilator of every nonempty subset of R is a
finitely generated right ideal. R is called a right CTF ring if every cyclic torsionless right R …

An exact sequence 0→ A→ B→ C→ 0 of left R-modules is called cyclically pure if for every
right ideal I of R, the sequence 0→(R/I)⊗ A→(R/I)⊗ B→(R/I)⊗ C→ 0 is exact. In this paper …