Add to ORKGAbstract. Let R be a commutative ring with non-zero identity. For a non-empty set PR of prime ideals of R, we study the class CR of R-modules A with the property that each weakly associated prime ideal of A belongs to PR. We show that CR is a torsion class for a hereditary torsion theory if and only if CR = R-Mod. Also, we prove that CR is a torsionfree class for some hereditary torsion theory, provided R is Artinian
Let R be a ring with identity, and let Mod-R be the category of right R-modules. Let M be a right R-...
We consider when a single submodule and also when every submodule of a module M over a general ring ...
AbstractAn ideal I of a commutative ring R with identity is said to be coprimely packed by prime ide...
AbstractNecessary and sufficient conditions are provided for the nilpotence of the intersection of a...
AbstractA right R-module M is non-singular if xI≠0 for all non-zero x∈M and all essential right idea...
Let R be an associative (not necessarily commutative) ring with unit. The study of flat left R-modul...
Let A be a commutative ring, and let \a := \frak{a} be a finitely generated ideal in it. It is known...
Cotorsion abelian groups form an important class of abelian groups for which nice structure theorems...
left R-modules to be an S-torsion theory if and only if there exists an ideal I of R satisfying the ...
R-modules are algebraic objects which may be considered as generalizations of k-vector spaces. An el...
Abstract. Recently, Rim and Teply [8], using the notion of τ-exact modules, found a nec-essary condi...
AbstractWe prove a uniqueness theorem for presentations of modules over a class of hereditary noethe...
The concepts of torsion and torsion-free objects have their origins in abelian group theory, where f...
An R module M is herein called torsion if each element has nonzero annihilator, and faithful if the ...
Let be a hereditary torsion theory. The purpose of this paper is to extend results about singular (...
Let R be a ring with identity, and let Mod-R be the category of right R-modules. Let M be a right R-...
We consider when a single submodule and also when every submodule of a module M over a general ring ...
AbstractAn ideal I of a commutative ring R with identity is said to be coprimely packed by prime ide...
AbstractNecessary and sufficient conditions are provided for the nilpotence of the intersection of a...
AbstractA right R-module M is non-singular if xI≠0 for all non-zero x∈M and all essential right idea...
Let R be an associative (not necessarily commutative) ring with unit. The study of flat left R-modul...
Let A be a commutative ring, and let \a := \frak{a} be a finitely generated ideal in it. It is known...
Cotorsion abelian groups form an important class of abelian groups for which nice structure theorems...
left R-modules to be an S-torsion theory if and only if there exists an ideal I of R satisfying the ...
R-modules are algebraic objects which may be considered as generalizations of k-vector spaces. An el...
Abstract. Recently, Rim and Teply [8], using the notion of τ-exact modules, found a nec-essary condi...
AbstractWe prove a uniqueness theorem for presentations of modules over a class of hereditary noethe...
The concepts of torsion and torsion-free objects have their origins in abelian group theory, where f...
An R module M is herein called torsion if each element has nonzero annihilator, and faithful if the ...
Let be a hereditary torsion theory. The purpose of this paper is to extend results about singular (...
Let R be a ring with identity, and let Mod-R be the category of right R-modules. Let M be a right R-...
We consider when a single submodule and also when every submodule of a module M over a general ring ...
AbstractAn ideal I of a commutative ring R with identity is said to be coprimely packed by prime ide...