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On a generalization of $Q I$ -rings

Josef Jirásko (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper rings for which every $s$ -torsion quasi-injective module is weakly $s$ -divisible for a hereditary preradical $s$ are characterized in terms of the properties of the corresponding lattice of the (hereditary) preradicals. In case of a stable torsion theory these rings coincide with $T Q I$ -rings investigated by J. Ahsan and E. Enochs in [1]. Our aim was to generalize some results concerning $Q I$ -rings obtained by J.S. Golan and S.R. L’opez-Permouth in [12]. A characterization of the $Q I$ -property in the...

On a variant of quasi-injectivity via kernel functors

Paramhans, S.A. (1988)

Portugaliae mathematica

On classical quotient rings of skew Armendariz rings.

Nasr-Isfahani, A.R., Moussavi, A. (2007)

International Journal of Mathematics and Mathematical Sciences

On module categories with nilpotent infinite radical

Otto Kerner, Andrzej Skowroński (1991)

Compositio Mathematica

On non singular p-inyective rings.

Yasuyuki Hirano (1994)

Publicacions Matemàtiques

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

J. Garcia, D. Simson (1997)

Colloquium Mathematicae

On rings with zero total.

Beidar, K.I. (1997)

Beiträge zur Algebra und Geometrie

On topologies over rings.

Fakhruddin, Syed M. (1985)

International Journal of Mathematics and Mathematical Sciences

On torsionfree classes which are not precover classes

Ladislav Bican (2008)

Czechoslovak Mathematical Journal

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 $μ$ -singular and $μ$ -extending modules

Yahya Talebi, Ali Reza Moniri Hamzekolaee (2012)

Archivum Mathematicum

Let $M$ be a module and $μ$ be a class of modules in $Mod - R$ which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a $μ$ -essential submodule provided it has a non-zero intersection with any non-zero submodule in $μ$ . We define and investigate $μ$ -singular modules. We also introduce $μ$ -extending and weakly $μ$ -extending modules and mainly study weakly $μ$ -extending modules. We give some characterizations of $μ$ -co-H-rings by weakly $μ$ -extending modules. Let $R$ ...

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