Let $ R $ be any ring and let $ M $ be any right $ R $-module. $ M $ is called hollow-lifting if
every submodule $ N $ of $ M $ such that $ M/N $ is hollow has a coessential submodule …

Let S be a unitary left module over a ring ℝ with 1. In this paper, we introduced the concept
of T-semihollow-lifting module as follows, an T-module F is T-semihollow-lifting if for each …

In studying injective covers, the modules C such that Hom (E, C)= 0 and Ext"(E, C)= 0 for all
injective module E play an important role because of Wakamatsu's lemma. If C is a module …

A module KR is said to be RL-subflat if for every short exact sequence 0→ U→ D→ L→ 0 of
left R-modules, the sequence 0→ K⊗ U→ K⊗ D→ K⊗ L→ 0 is exact. The subflat domains of …

A submodule N of a module M is called S-closed (in M) if M/N is nonsingular. It is well-known
that the class Closed of short exact sequences determined by closed submodules is a …

Let R be a ring, X a class of R-modules and n≥ 1 an integer. We introduce the concepts of
Gorenstein nX-injective and nX-flat modules via special finitely presented modules. Besides …

This paper extends many conclusions based on phantom envelopes and Ext-phantom
covers of modules, and we find that many important properties still hold after replacing …

A submodule $ N $ of a right R-module $ M $ is said to be $\tau $-dense in $ M $, if $ M/N $
is a $\tau $-torsion module. We shall denote the set of all $\tau $-dense right ideals of $ R …

Let R be a ring, and let n, d be non-negative integers. A right R-module M is called (n, d)-
projective if Ext d+ 1 R (M, A)= 0 for every n-copresented right R-module A. R is called right n …

Lomp [9] has studied finitely generated projective modules over semilocal rings. He
obtained the following: finitely generated projective modules over semilocal rings are …