Strongly irreducible submodules of modules are defined as follows: A submodule N of an R–
module M is said to be strongly irreducible if for submodules L and K of M, the inclusion L∩ …

Let R be a ring, n, d be fixed non-negative integers, the class of (n, d)-injective left R-
modules, and the class of (n, d)-flat right R-modules. In this paper, we prove that if R is a left …

We introduce the notion of almost pseudo-injective modules (AP-injective modules), which
generalizes the idea of pseudo-injective and almost injective modules. In support, we …

Let $ R $ be a ring and $ n $ a non-negative integer. In this paper, we first introduce the
concept of $ n $-super finitely copresented $ R $-modules and via these modules, we give a …

Let $ R $ be a ring, $ n $ be an non-negative integer and $ d $ be a positive integer or $\infty
$. A right $ R $-module $ M $ is called\emph {$(n, d)^* $-projective} if ${\rm Ext}^ 1_R (M …

For a fixed given right R-module M, so-called M-flat left R-modules are investigated, which
are flat relative to short exact sequences in the subcategory σ [M] subgenerated by M. The …

This paper unifies several generalizations of coherent rings in one notion. Namely, we
introduce nX-coherent rings, where X is a class of modules and n is a positive integer, as …

MODULES CHARACTERIZED BY THEIR SIMPLE SUBMODULES Lixin Mao According to
Nicholson and Watters [13], M is called a PS module if Page 1 TAIWANESE JOURNAL OF …

In this paper, we have introduced copure-direct-injective modules. A right R-module M is
said to be copure-direct-injective if every copure submodule of M isomorphic to a direct …

In this paper, we introduce the classes of strongly prime and one-sided strongly prime
submodules and use these classes to characterize Noetherian modules. A finitely generated …