scholarly journals L-Hollow modules

2019 ◽  
Vol 24 (7) ◽  
pp. 104
Author(s):  
Thaer Z. Khlaif ◽  
Nada K. Abdullah
Keyword(s):  
Commutative Ring ◽  
Strong Form ◽  
Fundamental Properties ◽  
Maximal Submodule

To consider R is a commutative ring with unity,  be a nonzero unitary left   R-module,  is known hollow module if each proper submodule of  is small.  L-hollow module is a strong form of hollow module, where an R-module  is known L-hollow module if  has a unique maximal submodule which contains each small submodules. The current study deals with this class of modules and give several fundamental properties  related with this concept.   http://dx.doi.org/10.25130/tjps.24.2019.136

The Intersection Property of Annihilators of Both Modules and Maximal Submodules Belonging to the Same Module

2020 ◽  
Vol 17 (2) ◽  
pp. 552-555
Author(s):  
Hatam Yahya Khalaf ◽  
Buthyna Nijad Shihab
Keyword(s):  
Commutative Ring ◽  
Intersection Property ◽  
Direct Sum ◽  
Unitary Module ◽  
Maximal Submodule ◽  
The Relationship

During that article T stands for a commutative ring with identity and that S stands for a unitary module over T. The intersection property of annihilatoers of a module X on a ring T and a maximal submodule W of M has been reviewed under this article where he provide several examples that explain that the property. Add to this a number of equivalent statements about the intersection property have been demonstrated as well as the direct sum of module that realize that the characteristic has studied here we proved that the modules that achieve the intersection property are closed under the direct sum with a specific condition. In addition to all this, the relationship between the modules that achieve the above characteristics with other types of modules has been given.

scholarly journals Coalgebras on Digital Images

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2082
Author(s):  
Sunyoung Lee ◽  
Dae-Woong Lee
Keyword(s):  
Commutative Ring ◽  
Digital Images ◽  
Continuous Functions ◽  
Contravariant Functor ◽  
Fundamental Properties

In this article, we investigate the fundamental properties of coalgebras with coalgebra comultiplications, counits, and coalgebra homomorphisms of coalgebras over a commutative ring R with identity 1R based on digital images with adjacency relations. We also investigate a contravariant functor from the category of digital images and digital continuous functions to the category of coalgebras and coalgebra homomorphisms based on digital images via the category of unitary R-modules and R-module homomorphisms.

scholarly journals S-maximal Submodules

2015 ◽  
Vol 12 (1) ◽  
pp. 210-220
Author(s):  
Baghdad Science Journal
Keyword(s):  
Commutative Ring ◽  
Jacobson Radical ◽  
Maximal Submodule

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings and modules. .

On the Maximal Spectrum of Semiprimitive Multiplication Modules

2008 ◽  
Vol 51 (3) ◽  
pp. 439-447
Author(s):  
Karim Samei
Keyword(s):  
Finite Number ◽  
Commutative Ring ◽  
Discrete Space ◽  
Multiplication Module ◽  
Prime Submodules ◽  
Maximal Submodule ◽  
Isolated Points ◽  
Maximal Spectrum ◽  
One Point Compactification

AbstractAnR-moduleMis called a multiplication module if for each submoduleNofM,N=IMfor some idealIofR. As defined for a commutative ringR, anR-moduleMis said to be semiprimitive if the intersection of maximal submodules ofMis zero. The maximal spectra of a semiprimitive multiplication moduleMare studied. The isolated points of Max(M) are characterized algebraically. The relationships among the maximal spectra ofM, Soc(M) and Ass(M) are studied. It is shown that Soc(M) is exactly the set of all elements ofMwhich belongs to every maximal submodule ofMexcept for a finite number. If Max(M) is infinite, Max(M) is a one-point compactification of a discrete space if and only ifMis Gelfand and for some maximal submoduleK, Soc(M) is the intersection of all prime submodules ofMcontained inK. WhenMis a semiprimitive Gelfand module, we prove that every intersection of essential submodules ofMis an essential submodule if and only if Max(M) is an almost discrete space. The set of uniform submodules ofMand the set of minimal submodules ofMcoincide. Ann(Soc(M))Mis a summand submodule ofMif and only if Max(M) is the union of two disjoint open subspacesAandN, whereAis almost discrete andNis dense in itself. In particular, Ann(Soc(M)) = Ann(M) if and only if Max(M) is almost discrete.

Total graph of the ring ℤn × ℤm

2015 ◽  
Vol 07 (01) ◽  
pp. 1550004 ◽  
Author(s):  
Alpesh M. Dhorajia
Keyword(s):  
Commutative Ring ◽  
Undirected Graph ◽  
Clique Number ◽  
Total Graph ◽  
Fundamental Properties ◽  
Zero Divisors ◽  
Independent Number ◽  
Positive Integers

Let R be a commutative ring and Z(R) be the set of all zero-divisors of R. The total graph of R, denoted by T Γ(R), is the (undirected) graph with vertices set R. For any two distinct elements x, y ∈ R, the vertices x and y are adjacent if and only if x + y ∈ Z(R). In this paper, we obtain certain fundamental properties of the total graph of ℤn × ℤm, where n and m are positive integers. We determine the clique number and independent number of the total graph T Γ(ℤn × ℤm).

scholarly journals Semi-T-maximal sumodules

2019 ◽  
pp. 2725-2731
Author(s):  
Inaam M. A. Hadi ◽  
Alaa A. Elewi
Keyword(s):  
Commutative Ring ◽  
Semisimple Module ◽  
Maximal Submodule

Let  be a commutative ring with identity and  be an -module. In this work, we present the concept of semi--maximal sumodule as a generalization of -maximal submodule. We present that a submodule  of an -module  is a semi--maximal (sortly --max) submodule if  is a semisimple -module (where  is a submodule of ). We  investegate some properties of these kinds of modules.

On quasi-radical of near-ring of polynomials

2019 ◽  
Vol 56 (2) ◽  
pp. 252-259
Author(s):  
Ebrahim Hashemi ◽  
Fatemeh Shokuhifar ◽  
Abdollah Alhevaz
Keyword(s):  
Commutative Ring ◽  
Nilpotent Elements ◽  
Ring Of Polynomials

Abstract The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.

Metastable Defects in the Amorphous Silicon-Germanium Alloys

2003 ◽  
Vol 762 ◽  
Author(s):  
J. David Cohen
Keyword(s):  
Amorphous Silicon ◽  
Silicon Germanium ◽  
Dangling Bonds ◽  
Annealing Behavior ◽  
Fundamental Properties ◽  
Silicon Materials ◽  
Salient Features ◽  
The Individual ◽  
Amorphous Silicon Germanium ◽  
Silicon Germanium Alloys

AbstractThis paper first briefly reviews a few of the early studies that established some of the salient features of light-induced degradation in a-Si,Ge:H. In particular, I discuss the fact that both Si and Ge metastable dangling bonds are involved. I then review some of the recent studies carried out by members of my laboratory concerning the details of degradation in the low Ge fraction alloys utilizing the modulated photocurrent method to monitor the individual changes in the Si and Ge deep defects. By relating the metastable creation and annealing behavior of these two types of defects, new insights into the fundamental properties of metastable defects have been obtained for amorphous silicon materials in general. I will conclude with a brief discussion of the microscopic mechanisms that may be responsible.

Sign in / Sign up

Export Citation Format

Share Document