We study the notion (for categories of modules) dual to that of torsion radical and its
connections with projective modules. Torsion radicals in categories of modules have been …

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 …

Singular left modules over an associative ring A are characterized by the fact that the
annihilator of every element is an essential left ideal. These modules play an important part …

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 …

Foxby duality has proven to be an important tool in studying the category of modules over a
local Cohen-Macaulay ring admitting a dualizing module. Recently the notion of a semi …

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 …

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 …

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 …

On rings with trivial torsion parts Page 1 BULL. AUSTRAL. MATH. SOC. I8A40 VOL. 9 (1973),
275-290. (I6AI2 ' 16A32) On rings with trivial torsion parts L. Bican, P. Jambor, T. Kepka, P …

The purpose of this paper is two-fold. First, we show that certain known properties of
associative radicals cannot be extended to the class of all rings. Secondly, we investigate …