A classical question for modules over an integral domain is," When is the torsion submodule
t (A) of a module A a direct summand of AT'A module is said to split when its torsion …

In this paper, we give some characterizations of FP-grinjective R-modules and graded right
R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective …

Let S and R be two associative rings, SCR be a faithfully balanced (S, R)-bimodule. We
introduce and investigate properties of∞-torsionfree modules with respect to SCR, which …

E. Enochs began the study of injective covers in [3], characterizing when any left Ä-module
has an injective cover. This happens if and only if R is a left noetherian ring. Torsion injective …

In this paper, we introduce and study regular rings relative to the hereditary torsion theory $
w $(a special case of a well-centered torsion theory over a commutative ring), called $ w …

Let I be an ideal of a commutative Noetherian ring R such that the R-modules HI i (U) are I-
cofinite, for all finitely generated R-modules U and all i∈ ℕ 0. Also, assume that the category …

Let R be a ring, τ= T, ℱ a hereditary torsion theory of mod‐R, and na positive integer. Then,
R is called right τ‐n‐coherent if every n‐presented right R‐module is (τ, n+ 1)‐presented …

A module M over a ring R is said to satisfy (P) if every generating set of M contains an
independent generating set. The following results are proved;(1) Let $\tau $=($\mathbb {T} …

The notion of an almost-precover as a generalization of a-precover is introduced. Among
other results it is shown that if is any hereditary torsion theory for the category R-mod, then …

The purpose of this paper is to develop a theory of cotorsion modules over a Noetherian
hereditary ring. In order to define a cotorsion theory one must first have a torsion theory …