1. Throughout this note, all rings will have unit elements and all modules will be unitary. By a
Noetherian ring, we shall mean a right Noetherian ring. A non-zero right ideal in a ring will …

A right artinian ring is a ring having an identity and satisfying the minimum condition for right
ideals. The main theme of this paper is the investigation of those rings which have a right …

1. It has been shown by Feller and Swokowski [I] that if R is an integral domain which has a
right and left quotient ring, then the endomorphism ring E (M) of a finitely generated torsion …

IN [5] PF Smith investigated those rings all of whose finitely-generated or cyclic modules
satisfy certain decomposition properties. For example he proved that every finitely …

The object of this paper is to study the relationship between certain projective modules and
their endomorphism rings. Specifically, the basic problem is to describe the projective …

In [2, page 151], J. Lambek proposes the following exercise: With any maximal right ideal M
of a ring R with 1 associate the ideal. Show that OM, is the right annihilator of the injective …

Throughout this paper, rings are associative with identity but are not necessarily
commutative, and modules are unitary right modules. An adjective which is not proceeded …

This is of course equivalent to the condition that every simple module is either projective or
injective. Theorem 1.1 gives necessary and sufficient conditions for a T-ring to have property …

In [3], Bass has shown that a ring R is left perfect if and only if every flat left R-module is
projective and if and only if R satisfies the descending chain condition on principal right …

One of the objectives of this paper is the examination of the relritionship between the
following properties of a Noetherian ring A:(i) every ideal of2 can be generated by two …