We study an R-module M in which every finitely generated submodule of M is a kernel of an
endomorphism of M. Such modules are called Co-epi-finite-retractable (CEFR). We also …

We first prove that if a monomorphism is a phantom envelope of a left R-module, then its
cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an Ext Ext …

Thuyet and Wisbauer considered the extending property for the class of (essentially) finitely
generated submodules. A module M is called ef-extending if every closed submodule which …

A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely
cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the …

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image
of M. It is shown that if R is a right perfect ring, then every projective slightly compressible …

Let R be a ring and M a left R-module. An R-module N is called a cofinite extension of M in
case and is finitely generated. We say that M has the property CE (resp. CEE) if M has a …

A module M is called EPI-RETRACTABLE if every submodule of M is a homomorphic image
of M. Dually, a module M is called co-EPI-RETRACTABLE if it contains a copy of each of its …

Let R be a commutative Noetherian ring, I an ideal of R and let M and N be non-zero R-
modules. It is shown that the R-modules ExtRi (N, M) are I-cofinite, for all i⩾ 0, whenever M is …

Let R be a ring. A right R-module M is called f-projective if Ext1 (M, N)= 0 for any f-injective
right R-module N. We prove that (F-proj, F-inj) is a complete cotorsion theory, where F-proj …

An R-module M is called weakly co-Hopfian if any injective endomorphism of M is essential.
The class of weakly co-Hopfian modules lies properly between the class of co-Hopfian and …