Let R be a ring. R is left coherent if each of its finitely generated left ideals is finitely
presented. R is called left generalized morphic if for every element a in R, l (a)= Rb for some …

In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

A left R-module M is said to be left singly injective if Ext R 1 (F/K, M)= 0 for any cyclic
submodule K of any finitely generated free left R-module F. In this paper, we study the notion …

Let R be a ring. For a fixed positive integer n, R is said to be left n-semihereditary in case
every n-generated left ideal is projective. R is said to be weakly n-semihereditary if each n …

Direct Product of Left Almost Rings Page 1 International Journal of Sciences: Basic and
Applied Research (IJSBAR) ISSN 2307-4531 (Print & Online) http://gssrr.org/index.php?journal=JournalOfBasicAndApplied …

In this paper, we obtain that a commutative ring R is w-coherent if and only if Hom R (M, E) is
w-flat for any absolutely pure w-module M and any injective (w-) module E, if and only if Hom …

A ring R is called NZI if for any a\in R, l (a) is an N-ideal of R. In this paper, we first study
some basic properties and basic extensions of NZI rings. Next, we study the strong regularity …

A ring R is called a right ACS-ring if the annihilator of any element in R is essential in a direct
summand of R. In this note we will exhibit some elementary but important examples of ACS …

An element $ a $ in a ring R is called left morphic if $$ R/Ra {\simeq_-} 1 (a) $$. A ring is
called left morphic if every element is left morphic. In this paper, an element $ a $ in a ring R …

In this paper, we first study some characterizations of left MC2 rings. Next, by introducing left
nil-injective modules, we discuss and generalize some well known results for a ring whose …