Modules which are invariant under nilpotents of their envelopes and covers
A module is called nilpotent-invariant if it is invariant under any nilpotent endomorphism of
its injective envelope [MT Koşan and TC Quynh, Nilpotent-invaraint modules and rings …
its injective envelope [MT Koşan and TC Quynh, Nilpotent-invaraint modules and rings …
t-Nilpotent invariant modules
S Ebrahimi Atani, S Dolati Pish Hesari… - Communications in …, 2018 - Taylor & Francis
We introduce the notion of a t-nilpotent endomorphism of modules and study the modules
which are invariant under t-nilpotent endomorphisms of their injective envelope, such as …
which are invariant under t-nilpotent endomorphisms of their injective envelope, such as …
Nilpotent-invariant modules and rings
Automorphism-invariant modules, due to Lee and Zhou, generalize the notion of quasi-
injective modules. A module which is invariant under automorphisms of its injective hull is …
injective modules. A module which is invariant under automorphisms of its injective hull is …
On characterizations and properties of nil-injective rings and modules
FA Ahmed, AM Abdul-Jabbar - AIP Conference Proceedings, 2023 - pubs.aip.org
A special type of injective module which is introduced by Ming is called p-injective if for
every a∈ R, every R-linear map from aR to M can be extended to a linear map from R to M …
every a∈ R, every R-linear map from aR to M can be extended to a linear map from R to M …
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 …
Direct injective modules
C Zhizhong - Acta Mathematica Sinica, 1993 - Springer
Throughout this paper R will denote a ring with idenity element and M a unitary right module
over R. An R-module M is said to be direct injective if and only if given direct summand N of …
over R. An R-module M is said to be direct injective if and only if given direct summand N of …
On essential extensions of direct sums of either injective or projective modules
For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum
of injective right R-modules is injective, and R is right Noetherian if and only if every …
of injective right R-modules is injective, and R is right Noetherian if and only if every …
[PDF][PDF] Minimal quasi-injective modules
Z Zhu, Z Tan - Scientiae Mathematicae Japonicae, 2005 - jams.or.jp
Let R be a ring. A right R-module M is called minimal quasi-injective if every homomorphism
from a simple submodule of M to M can be extended to an endomorphism of M. Some …
from a simple submodule of M to M can be extended to an endomorphism of M. Some …
Direct sum decompositions of projective and injective modules into virtually uniserial modules
M Behboodi, A Moradzadeh-Dehkordi… - Revista de la Real …, 2022 - Springer
A theorem due to Warfield states that “a ring R is left serial if and only if every (finitely
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …
Phantom Envelopes and -Phantom Covers of Modules
L Mao - Bulletin of the Iranian Mathematical Society, 2020 - Springer
We first prove that if a monomorphism is a phantom envelope of a left R-module, then its
cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an Ext Ext …
cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an Ext Ext …