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 …

The concept of a torsion theory (𝒯, ℱ) for left R-modules has been defined by SE Dickson. A
torsion theory is called splitting if it has the property that the torsion submodule of every left R …

A classical question for modules over an integral domain is," When is the torsion submodule
t (A) of a module A a direct summand of AT'A module is said to split when its torsion …

Throughout this paper rings are commutative with identity and modules are unital. The
purpose of this paper is to study splitting properties of modules with respect to their torsion …

Injective and projective modules are studied relative to a hereditary torsion theory τ on Mod–
R. It is shown that every τ–projective module is projective if and only if the torsion ideal of R …

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 …

Modules with Unique Closure Relative to a Torsion Theory Page 1 Canad. Math. Bull. Vol. 53
(2), 2010 pp. 230–238 doi:10.4153/CMB-2010-012-9 c©Canadian Mathematical Society 2009 …

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 …

Modules With Unique Closure Relative to a Torsion Theory II Page 1 Turkish Journal of
Mathematics Volume 33 Number 2 Article 2 1-1-2009 Modules With Unique Closure Relative …

In the previous paper [g] we have introduced the notion of a cyclic-hereditary torsion class
for the category mod-R of unital right R-modules over a ring R with unit as a torsion class …