Preferred Language
Articles
/
ijs-6622
Purely Small Submodules and Purely Hollow Modules
...Show More Authors

         The main goal of this paper is to give  a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of  purely hollow modules is considered.

Scopus Crossref
View Publication Preview PDF
Quick Preview PDF
Publication Date
Sun Mar 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Purely Goldie Extending Modules
...Show More Authors

An -module  is extending if every submodule of   is essential in a direct summand of . Following Clark, an -module  is purely extending if every submodule of   is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module     is Goldie extending if, for each submodule      of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module  is purely Goldie extending if, for each , there is a pure submodule P of such that  . Many c

... Show More
View Publication Preview PDF
Publication Date
Tue Aug 31 2021
Journal Name
Iraqi Journal Of Science
Z-Small Submodules and Z-Hollow Modules
...Show More Authors

A submodule Ϝ of an R-module Ε is called small in Ε if whenever  , for some submodule W of Ε , implies  . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if  , such that  , then  , where  is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .

View Publication Preview PDF
Scopus (3)
Crossref (2)
Scopus Crossref
Publication Date
Wed May 10 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Purely co-Hopfian Modules
...Show More Authors

  Let R be an associative ring with identity and M a non – zero unitary R-module.In this paper we introduce the definition of purely co-Hopfian module, where an R-module M is said to be purely co-Hopfian if for any monomorphism f Ë› End (M), Imf is pure in M and we give  some properties of this kind of modules.

View Publication Preview PDF
Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
On Purely –Extending Modules
...Show More Authors

In this note we consider a generalization of the notion of a purely extending
modules, defined using y– closed submodules.
We show that a ring R is purely y – extending if and only if every cyclic nonsingular
R – module is flat. In particular every nonsingular purely y extending ring is
principal flat.

View Publication Preview PDF
Publication Date
Sat Apr 30 2022
Journal Name
European Journal Of Pure And Applied Mathematics
e*-Essential small submodules and e*-hollow module
...Show More Authors

Publication Date
Fri Dec 08 2023
Journal Name
Iraqi Journal Of Science
Modules With Chain Conditions On δ -Small Submodules
...Show More Authors

Let R be an associative ring with identity and M be unital non zero R-module. A
submodule N of a module M is called a δ-small submodule of M (briefly N << M )if
N+X=M for any proper submodule X of M with M/X singular, we have
X=M .
In this work,we study the modules which satisfies the ascending chain condition
(a. c. c.) and descending chain condition (d. c. c.) on this kind of submodules .Then
we generalize this conditions into the rings , in the last section we get same results
on δ- supplement submodules and we discuss some of these results on this types of
submodules.

View Publication Preview PDF
Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Interdisciplinary Mathematics
Pr-small R-submodules of modules and Pr-radicals
...Show More Authors

The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

Scopus (1)
Scopus Clarivate Crossref
Publication Date
Fri Jan 01 2010
Journal Name
Iraqi Journal Of Science
PRIME HOLLOW MODULES
...Show More Authors

A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.

View Publication Preview PDF
Publication Date
Sat Jul 31 2021
Journal Name
Iraqi Journal Of Science
Semi-T-Hollow Modules and Semi-T-Lifting Modules
...Show More Authors

Let be an associative ring with identity and let be a unitary left -module. Let  be a non-zero submodule of .We say that  is a semi- - hollow module if for every submodule  of  such that  is a semi- - small submodule ( ). In addition, we say that  is a semi- - lifting module if for every submodule  of , there exists a direct summand  of  and  such that  

The main purpose of this work was to develop the properties of these classes of module.

 

View Publication Preview PDF
Scopus Crossref
Publication Date
Thu May 04 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Strongly (Comletely) Hollow Submodules I
...Show More Authors

Let R be a commutative ring with unity and let M be an R-module. In this paper we
study strongly (completely) hollow submodules and quasi-hollow submodules. We investigate
the basic properties of these submodules and the relationships between them. Also we study
the be behavior of these submodules under certain class of modules such as compultiplication,
distributive, multiplication and scalar modules. In part II we shall continue the study of these
submodules.

View Publication Preview PDF