[图书][B] Lifting modules: supplements and projectivity in module theory
Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …
generalize projective supplemented modules. There is a certain asymmetry in this duality …
Small-Essential Submodules and Morita Duality.
DX Zhou, XR Zhang - Southeast Asian Bulletin of …, 2011 - search.ebscohost.com
We introduce and investigate e-small and s-essential submodules, and prove that Rad<
sub> e(M)=∩{N⊴ M/N is maximal in M}=∑{N⊆ M/N≪< sub> e M} and Soc< sub> …
sub> e(M)=∩{N⊴ M/N is maximal in M}=∑{N⊆ M/N≪< sub> e M} and Soc< sub> …
δ-lifting and δ-supplemented modules
MT Koşan - Algebra colloquium, 2007 - World Scientific
In this paper, δ-lifting and δ-supplemented modules are defined as generalizations of lifting
and supplemented modules. Several properties of these modules are proved. New …
and supplemented modules. Several properties of these modules are proved. New …
Semiregular, semiperfect and perfect rings relative to an ideal
MF Yousif, Y Zhou - The Rocky Mountain journal of mathematics, 2002 - JSTOR
Let I be an ideal of a ring R. Consider the following conditions on R: 1. If X is a finitely
generated submodule of a finitely generated projective module P, then X= A⨁ B where is a …
generated submodule of a finitely generated projective module P, then X= A⨁ B where is a …
Generalizations of supplemented and lifting semimodules
AH Alwan - Iraqi Journal of Science, 2024 - ijs.uobaghdad.edu.iq
In this paper, principally supplemented (-supplemented), and principally lifting (-lifting)
semimodules are defined as generalizations of principally supplemented (-supplemented) …
semimodules are defined as generalizations of principally supplemented (-supplemented) …
Weak Hopfcity and singular modules
A El Moussaouy, ARM Hamzekolaee, MH Ziane… - … DELL'UNIVERSITA'DI …, 2022 - Springer
The concept of Hopfian modules has been extensively studied in the literature. In this paper,
we introduce and study the notion of δ-weakly Hopfian modules. The class of δ-weakly …
we introduce and study the notion of δ-weakly Hopfian modules. The class of δ-weakly …
Some Variations of δ‐Supplemented Modules with Regard to a Hereditary Torsion Theory
J Tian, E Ozturk Sozen… - Journal of …, 2023 - Wiley Online Library
In present work, we describe and investigate torsion theoretic versions of δ‐supplemented
modules via a hereditary torsion theory τ. With this aim, first, we define δτ‐small …
modules via a hereditary torsion theory τ. With this aim, first, we define δτ‐small …
δ‐Small Submodules and δ‐Supplemented Modules
Y Wang - … Journal of Mathematics and Mathematical Sciences, 2007 - Wiley Online Library
Let R be a ring and M a right R‐module. It is shown that (1) δ (M) is Noetherian if and only if
M satisfies ACC on δ‐small submodules;(2) δ (M) is Artinian if and only if M satisfies DCC on …
M satisfies ACC on δ‐small submodules;(2) δ (M) is Artinian if and only if M satisfies DCC on …
[PDF][PDF] On a class of δ-supplemented modules
Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a
class of modules which is an analogous to δsupplemented modules and principally⊕ …
class of modules which is an analogous to δsupplemented modules and principally⊕ …
When\delta-semiperfect rings are semiperfect
E Büyükaşik, C Lomp - Turkish journal of mathematics, 2010 - journals.tubitak.gov.tr
Zhou defined\delta-semiperfect rings as a proper generalization of semiperfect rings. The
purpose of this paper is to discuss relative notions of supplemented modules and to show …
purpose of this paper is to discuss relative notions of supplemented modules and to show …