For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

In a recent paper, Mao has studied min-pure injective modules to investigate the existence
of min-injective covers. A min-pure injective module is one that is injective relative only to …

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 …

R is called a left PS (resp. left min-coherent, left universally mininjective) ring if every simple
left ideal is projective (resp. finitely presented, a direct summand of R). We first investigate …

Abstract A right R-module M is called R-projective provided that it is projective relative to the
right R-module R R. One of the parts of this thesis deals with the rings whose all nonsingular …

Min-injective rings and min-injective modules has a substantial role in module-ring theory
and representations of algebras. Numerous characterizations of Quasi-Frobenius rings were …

Recall that a ring R is said to be left coherent [2, 7] if every finitely generated left ideal of R is
finitely presented, a ring R is said to be left semihereditary if every finitely generated left …

Let $ R $ be a ring and $\mathscr {C} $ be a class of some finitely presented left $ R $-
modules. A left $ R $-module $ M $ is called $\mathscr {C} $-injective if Ext $^ 1_R (C, M) …

Min-Flat Dimensions and Min-Flat Rings 1 Introduction 2 Preliminary Notes Page 1 Int. J.
Contemp. Math. Sciences, Vol. 5, 2010, no. 18, 877 - 883 Min-Flat Dimensions and Min-Flat …

Let M be a left R-module, AA be a family of some submodules of M and BB be a family of
some left R-modules. In this article, we introduce and characterize A A-coherent, PA PA, FA …