On a variant of quasi-injectivity via kernel functors
On classical quotient rings of skew Armendariz rings.
On module categories with nilpotent infinite radical
On non singular p-inyective rings.
A ring R is said to be left p-injective if, for any principal left ideal I of R, any left R-homomorphism I into R extends to one of R into itself. In this note left nonsingular left p-injective rings are characterized using their maximal left rings of quotients and the structure of semiprime left p-injective rings of bounded index is investigated.
On rings whose flat modules form a Grothendieck category
On rings with zero total.
On topologies over rings.
On torsionfree classes which are not precover classes
In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite...
On -singular and -extending modules
Let be a module and be a class of modules in which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a -essential submodule provided it has a non-zero intersection with any non-zero submodule in . We define and investigate -singular modules. We also introduce -extending and weakly -extending modules and mainly study weakly -extending modules. We give some characterizations of -co-H-rings by weakly -extending modules. Let ...
Precovers
Let be an abstract class (closed under isomorpic copies) of left -modules. In the first part of the paper some sufficient conditions under which is a precover class are given. The next section studies the -precovers which are -covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left -modules. Especially, several sufficient conditions for the existence of -torsionfree and -torsionfree -injective covers are presented.
Precovers and Goldie’s torsion theory
Recently, Rim and Teply , using the notion of -exact modules, found a necessary condition for the existence of -torsionfree covers with respect to a given hereditary torsion theory for the category -mod of all unitary left -modules over an associative ring with identity. Some relations between -torsionfree and -exact covers have been investigated in . The purpose of this note is to show that if is Goldie’s torsion theory and is a precover class, then is a precover class whenever...
Preradicals and generalizations of - modules. I.
Preradicals and generalizations of - modules. II.
Pseudohereditary and pseudocohereditary preradicals
QTAG torsionfree modules
The structure theory of abelian -groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated -group is a direct sum of cyclics. Given a hereditary torsion theory on the category -Mod of unitary left -modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This...
Quelques remarques sur la notion d'extension rationnelle maximale d'un module et sur les anneaux maximaux de fractions au sens d'Utimi
Quotients of reflexive modules
Radicals which define factorization systems
A method due to Fay and Walls for associating a factorization system with a radical is examined for associative rings. It is shown that a factorization system results if and only if the radical is strict and supernilpotent. For groups and non-associative rings, no radical defines a factorization system.
Rad-supplemented modules
Relative coherence and preenvelopes.