This paper is concerned with studying necessary and sufficient conditions on a ring [italic] R
such that for certain classes of right [italic] R-modules, the singular submodule of any …

The idea of a torsion element of an abelian group extends naturally enough to modules over
integral domains, but for modules over an arbitrary ring there seem to be a number of …

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 …

Let M and N be R-modules. We define where S denotes the class of all M-small modules.
We call N an M-cosingular (non-M-cosingular) module if ZM (N)= 0 (ZM (N)= N). We study …

Using SE Dickson's characterization of a torsion class, a class of modules closed under
taking factors extensions and arbitrary direct sum, we study torsion classes closed under …

When we consider modules A over a ring R which is not a commutative integral domain, the
usual torsion theory becomes somewhat inadequate, since zero-divisors of R are …

In trying to extend the concept of torsion to rings more general than commutative integral
domains the first thing that we notice is that if the definition is carried over word for word …

In a celebrated theorem, AW Goldie determined necessary and sufficient conditions that a
ring have a left quotient ring which is semisimple with minimum condition [4]. Our first main …

Torsionfree injective modules Page 1 Pacific Journal of Mathematics TORSIONFREE
INJECTIVE MODULES MARK LAWRENCE TEPLY Vol. 28, No. 2 April 1969 Page 2 PACIFIC …

THEOREM. Let R be an unramified regular local ring, and M a torsion-free R-module of finite
type./f Tor (M, N) 0 for some R-module N offinite type, then Tor M, N) 0 for all j>= i. In this …