The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the
construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really …

This book is an account of a certain portion of noncommutative ring theory which originated
in the work of RE Johnson [113, 115], who introduced nonsingular rings, in 1951, and …

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 …

Let K be a convex set in a lcs and A a convex subset in the closure of K. It is shown in § 1
that, in certain cases, the exposed points of A belong to the sequential closure of K …

A torsion theory for a module cate6: ory is called splitting provided the torsion submodule of
every module is a direct sw.-mand and centrally splitting provided there exists a central …

The 𝒯-divisible R-modules are defined in terms of a hereditary torsion theory of modules
over an associative ring R with identity element. In the special case where 𝒯 is the usual …

Given a hereditary torsion functor, the class of μ-complemented modules was recently
introduced by PF Smith and the authors as an analogue of extending modules. This current …

Let (𝒯, ℱ) denote a hereditary torsion theory for the category of modules over a ring R. In this
paper the splitting of projective modules is studied, and it is shown that this is not equivalent …

Rings Characterized by Their Torsion Cyclic Modules Page 1 HOUSTON JOURNAL OF
MATHEMATICS, Volume 14, No. 3, 1988. RINGS CHARACTERIZED BY THEIR TORSION …

Throughout this paper R is a ring with a unit element, every right R-module is unital and Mod-
R is the category of right R-modules. A subfunctor of the identity functor of Mod-R is called a …