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 …

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 …

Goldie's torsion class 𝒢 is a class of left R-modules closed under taking submodules, factor
modules, extensions, arbitrary direct sums, and injective envelopes. The corresponding …

Because F is a free module of infinite rank we see that F^ Fn all n^ l. It follows that H^ Hn as
right (or left) H-modul es. So H is isomorphic (as ring) to Hn, forali n> 1. Further every finitely …

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 …

Let A be an integral domain and R its field of fractions. An A-module E is said to be torsion
free if ox= 0 for ctEA, xEE implies a= 0 or x= 0. We will say that a submodule£ i of an A …

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 …

We always let R denote a ring with identity element. All modules will be unital left R-
modules. We use IXI to denote the cardinality of a set X. If A is a set and Ma (aeA) are …

Free ideal rings (FIRs) introduced in (4) form a natural generalization of principal ideal
domains (PIDs), to which they reduce in the commutative case. However, they include many …

Introduction. Let R be an associative ring with identity and let r9JJ (respectively Wr) denote
the category of unitary left (respectively right) P-modules. Dickson [4] has given an axiomatic …