Let Rbe a ring with identity. Chase [5] has characterized the right coherent rings; he has
shown that arbitrary products of RR are flat if and only if finitely generated submodules of …

Throughout this paper R will be a commutative ring with one, and all R-modules will be
unitary. Our purpose is to study commutative ring exten-sions S of R. As a key tool in our …

1. Introduction. Let R be a ring (associative and with identity). It is easy to see that every left
ideal of R is the (left) annihilator of a finite subset of R if and only if every cyclic left R-module …

Let R be a ring with identity. As in [I],[XI, and [= I, a class T of leftd (or right) R-modules is
called a torsion class if it is closed under direct sums, homomorphic images, and extensions …

We study, over an arbitrary ring R, a class of right modules intermediate between the
projective and the flat content modules. Over the ring of rational integers these modules are …

In Morita's paper [-4] he investigates the torsion theory and the quotient ring arising from a
flat module. If RU is a flat module then one can consider as torsion all modules MR such that …

T (M)=(x= M| Hom,(Ra, I (R))= 0) where I (R) is the injective hull of R as a left R-module. A left
R-module M is said to be torsion free if T (M)= 0. For the properties of torsion free modules …

In this note we characterize those torsion theories over a semiperfect ring such that the class
of torsion free modules is closed under projective covers and the hereditary torsion theories …

Throughout this paper it is assumed that rings are associative, have the identity element,
and all modules are left unital. R will denote a ring with identity, R-Mod the category of left R …

Rings for which every singular left module is injective, called SI-rings, were introduced and
studied by Goodearl [4]. He characterized such rings as those nonsingular ones for which …