For an arbitrary left R-module M, we denote by F (M) the class of left R-modules F such that
for any exact sequence 0→ A α→ B of left R-modules and any R-homomorphism β: A→ M …

Abstract A right R-module M is called:(1) retractable if Hom R (M, N)≠ 0 for any non-zero
submodule N of M;(2) coretractable if Hom R (M/N, M)≠ 0 for any proper submodule N of M …

In [1], PE Bland has studied the strongly M-projective module and the strongly M-projective
cover. As their generalnotions, we define the strongly $\eta $-projective module and the …

Let R be a noetherian ring, and denote the full subcategories of R-modules L such that Exti
(E, L)= 0 for all injective R-modules E for 1⋚ i⋚ n and O⋚ i⋚ n by Cn, and C′ n respectively …

Endomorphism rings and the category of finitely generated projective modules Page 1
COMMLTNICATIONS IN ALGEBRA, 28(8), 3837-3 852 (2000) Endomorphism rings and the …

Let M and N be right R-modules. Hom (M, N) is called regular if for each f∈ Hom (M, N),
there exists g∈ Hom (N, M) such that f= fgf. Let [M, N]= Hom R (M, N). We prove that if M is …

Given a semiperfect two-sided noetherian ring Λ, we study two subcategories $ 𝓐_k
(Λ)={M∈ mod Λ| Ext_ {Λ}^{j}(Tr M, Λ)= 0 (1≤ j≤ k)} $ and $ 𝓑_k (Λ)={N∈ mod Λ| Ext …

In this paper, we show the existence of copure injective preenvelopes over noetherian rings
and copure flat preenvelopes over commutative artinian rings. We use this to characterize …

Let A and B be commutative Noetherian local rings, such that B is a finitely generated free A-
module. It is shown that if M is a balanced big Cohen–Macaulay A-module (that is, every …