Prime–Extending Module and S-Prime Module

2011 ◽  
Vol 14 (4) ◽  
pp. 166-170
Author(s):  
Tamadher A. Ibrahiem ◽  
Keyword(s):  
Prime Module ◽  
Extending Module

scholarly journals On small (T-extending) module

2020 ◽  
Vol 1530 ◽  
pp. 012059
Author(s):  
Zainab Rzaij Mohammad ◽  
Sahira Mahmood Yassin
Keyword(s):  
Extending Module

scholarly journals ON RICKART MODULES

2019 ◽  
pp. 2473-2477
Author(s):  
Mohammed Qader Rahman ◽  
Bahar Hamad Al-Bahrani
Keyword(s):  
Prime Module ◽  
Rickart Modules

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules. The main purpose of this paper is to develop the properties of Rickart modules . We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

Development and Design of LonWorks Intelligent Nodes

2012 ◽  
Vol 542-543 ◽  
pp. 1037-1041
Author(s):  
Shu Ya Zhi ◽  
An Bang Gao
Keyword(s):  
Hardware Design ◽  
Single Chip ◽  
Single Chip Microcomputer ◽  
Utility Value ◽  
Field Bus ◽  
Extending Module

This paper introduces how to develop and design multiple I/O nodes using the LonWorks field-bus technology, which is based on the mainframe (single chip microcomputer). It deals with the distribution of MIO nodes, the hardware design of TP/FT-10F master controlling module, the design of VCN-MIO platter and extending module(digital, analog), the trouble diagnose of nodes, and the anti-disturbance design. It has important utility value.

scholarly journals Some Results on Pure Submodules Relative to Submodule

2015 ◽  
Vol 12 (4) ◽  
pp. 833-837
Author(s):  
Baghdad Science Journal
Keyword(s):  
Commutative Ring ◽  
Extending Module ◽  
Closed Submodules ◽  
Pure Submodules

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

scholarly journals SIFAT KEPRIMAAN MODUL SEDERHANA CHEN UNTUK GRAF 𝐴∞

2019 ◽  
Vol 12 (2) ◽  
Author(s):  
Risnawita Risnawita ◽  
Irawati Irawati ◽  
Intan Muchtadi Alamsyah
Keyword(s):  
Directed Graph ◽  
Infinite Sequence ◽  
Line Graph ◽  
Simple Module ◽  
Path Algebra ◽  
Leavitt Path Algebra ◽  
Directed Line ◽  
Simple Modules ◽  
Infinite Path ◽  
Prime Module

Let 𝐾𝐾 be a field, 𝐸𝐸 is a directed graph. Let 𝐴𝐴~ is a directed line graph. Suppose that 𝑉𝑉[𝑝𝑝] is a class of Chen simple module for the Leavitt path algebra (𝐿𝐿𝐾𝐾 (𝐸𝐸)), with [p] being equivalent classes containing an infinite path. An infinite path p is an infinite sequence from the sides of a graph. In this paper it will be shown that 𝑉𝑉[𝑝𝑝]is not a prime module of the Leavitt path algebra for graph 𝐴𝐴∞ .Keywords : Leavitt path algebra, Graph 𝐴𝐴~, Chen simple modules, Prime modules

scholarly journals Relationship of Essentially Small Quasi-Dedekind Modules with Scalar and Multiplication Modules

2020 ◽  
pp. 179-182
Author(s):  
Inas Salman Obaid ◽  
Mukdad Qaess Hussain ◽  
Darya Jabar AbdulKareem
Keyword(s):  
Dedekind Ring ◽  
Multiplication Module ◽  
Left Module ◽  
Prime Module ◽  
Relationship Of ◽  
The Relationship

Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.

scholarly journals weakly supplement extending modules

2020 ◽  
Vol 31 (2) ◽  
pp. 38
Author(s):  
Saad A. Al-Saadi ◽  
Aya Adnan Musa
Keyword(s):  
Direct Sum ◽  
Closed Submodule ◽  
Extending Module ◽  
Supplement Submodule

In this paper, the extending property of modules is generalized by using weakly supplement submodules. We call a module M is weakly supplement extending if each submodule of M is essential in a weakly supplement submodule of M. Many characterization of weakly supplement extending module are obtained, we show that M is weakly supplement extending if and only if each closed submodule is weakly supplementing submodule of M. Moreover, we study the relation of weakly supplement extending module and among other known classes of the module such as lifting module, weakly supplemented module, supplement extending module and others. Also, we study conditions under it a direct sum of weakly supplement extending module is weakly supplement extending. 

The set of singular elements of a ring with respect to a module

2018 ◽  
Vol 13 (03) ◽  
pp. 2050050
Author(s):  
A. Farzi–Safarabadi ◽  
R. Beyranvand
Keyword(s):  
Matrix Ring ◽  
Triangular Matrix ◽  
Semisimple Module ◽  
Prime Module ◽  
Triangular Matrix Ring ◽  
Singular Ideal ◽  
The Right

Let [Formula: see text] be a ring and [Formula: see text] be a right [Formula: see text]-module. In this paper, we introduce the set [Formula: see text] for some essential submodule [Formula: see text] of [Formula: see text] of singular elements of[Formula: see text] with respect to[Formula: see text] , and we investigate the properties of it. For example, it is shown that [Formula: see text] is an ideal of [Formula: see text] and [Formula: see text]. Also if [Formula: see text] is a semiprime right Goldie ring, then [Formula: see text], where [Formula: see text] is the right singular ideal of [Formula: see text]. We prove that if [Formula: see text] is a semisimple module or a prime module, then [Formula: see text]. For any submodule [Formula: see text] of [Formula: see text], we have [Formula: see text] and if [Formula: see text], then [Formula: see text]. We show that [Formula: see text] and [Formula: see text]. In the end, the singular elements of some rings with respect to the formal triangular matrix ring are investigated.

scholarly journals Strongly Weakly Supplement Extending Modules

2020 ◽  
Vol 30 (4) ◽  
pp. 71
Author(s):  
Aya Adnan Musa ◽  
Saad A. Al-Saadi
Keyword(s):  
Direct Sum ◽  
Closed Submodule ◽  
Extending Module ◽  
Supplement Submodule ◽  
Strong Concept

In this paper, a class of modules which are proper strong concept of weakly supplement extending modules will be introduced and studied. We call a module M is strongly weakly supplement extending, if each submodule of M is essential in fully invariant weakly supplement submodule in M. Many characterizations of strongly weakly supplement extending modules are obtained. We show that M is strongly weakly supplement extending module if and only if every closed submodule of M is fully invariant weakly supplement submodule in M. Also we study the relation among this concept and other known concepts of modules. Moreover, we give some conditions that of strongly weakly supplement extending modules is closed under direct sum property is strongly weakly supplement extending.

scholarly journals Dual of Extending Acts

2020 ◽  
pp. 64-71
Author(s):  
Shaymaa Amer Abdul Kareem
Keyword(s):  
Ring Theory ◽  
Research Interest ◽  
Major Area ◽  
Module Theory ◽  
Extending Module ◽  
Rees Factor

Since 1980s, the study of the extending module in the module theory has been a major area of research interest in the ring theory and it has been studied recently by several authors, among them N.V. Dung, D.V. Huyn, P.F. Smith and R. Wisbauer. Because the act theory signifies a generalization of the module theory, the author studied in 2017 the class of extending acts which are referred to as a generalization of quasi-injective acts. The importance of the extending acts motivated us to study a dual of this concept, named the coextending act. An S-act MS is referred to as coextending act if every coclosed subact of Ms is a retract of MS where a subact AS of MS is said to be coclosed in MS if whenever the Rees factor ⁄ is small in the Rees factor ⁄then AS=BS for each subact BS of AS. Various properties of this class of acts have been examined. Characterization of this concept is intended to show the behavior of a coextending property. In addition, based on the results obtained by us, the conditions under which subacts inherit a coextending property were demonstrated. Ultimately, a part of this paper

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