In this paper, the notions of f-injective and f*-injective modules are introduced. Elementary
properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct …

Let R be a ring and M be an R-module. M is said to be an E-module (respectively, an EE-
module) if M has a supplement (respectively, ample supplements) in every coatomic …

A ring R is said to be left n-semihereditary, if every n-generated left ideal of R is projective. It
is shown that for a ring R, the following statements are equivalent:(1) R is left n …

A ring A is a completely integrally closed right A-module if and only if the maximal right ring
of quotients Q max (A) of A is an injective right A-module and A is a right completely …

Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to
provide two new characterizations of coherent rings. The first of these characterizations …

We introduce and investigate t-continuous modules. A module M is called t-continuous if M
is t-extending, and every submodule of M which contains Z 2 (M) and is isomorphic to a …

A module $ M $ is called a $ C_ {21} $-module if, whenever $ A $ and $ B $ are submodules
of $ M $ with $ A\cong B $, $ A $ is nonsingular and $ B $ is a direct summand of $ M $, then …

It is well-known that a ring R is right PF if and only if it is semiperfect and right self-injective
with essential right socle. In this note, it is shown that a ring R is right PF if and only if u. dim …

right (left) closed ideal is a direct summand[6]. zero right (left) ideal is essential in a direct
summand, equivalently, every Page 1 Raf. J. of Comp. & Math’s. , Vol. 5, No. 2, 2008 193 On …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …