Rings characterized via some classes of almost-injective modules
In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …
Semisimple-direct-injective modules
The notion of simple-direct-injective modules which are a generalization of injective
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …
Rings for which every simple module is almost injective
S Asgari, M Arabi-Kakavand… - Bulletin of the Iranian …, 2016 - bims.iranjournals.ir
We introduce the class of “right almost V-rings” which is properly between the classes of
right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R …
right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R …
On a class of QI-rings
SK Jain, SR López-Permouth, S Singh - Glasgow Mathematical …, 1992 - cambridge.org
The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …
On simple-injective modules
Y Alagöz, S Benli̇-Göral… - Journal of Algebra and its …, 2023 - World Scientific
For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …
every cyclic right module N. The rings whose simple-injective right modules are injective are …
[HTML][HTML] Virtually uniserial modules and rings
M Behboodi, A Moradzadeh-Dehkordi, MQ Nejadi - Journal of Algebra, 2020 - Elsevier
We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …
On rings with cyclic almost-injective modules
It is shown that every finitely generated right R-module is almost injective if and only if every
cyclic right R-module is almost injective, if and only if R/J (R) is a right SV-ring with Loewy …
cyclic right R-module is almost injective, if and only if R/J (R) is a right SV-ring with Loewy …
A generalization of uniserial modules and rings
S Shirzadi, R Beyranvand… - arXiv preprint arXiv …, 2023 - arxiv.org
We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …
The opposite of injectivity by proper classes
Proper classes (or exact structures) offer rich research topics due to their important role in
category theory. Motivated by the studies on opposite of injective modules, we introduce a …
category theory. Motivated by the studies on opposite of injective modules, we introduce a …
[HTML][HTML] Simple-direct-injective modules
A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …