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Rationally Extending Modules and Strongly Quasi-Monoform Modules
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An R-module M is called rationally extending if each submodule of M is rational in a direct summand of M. In this paper we study this class of modules which is contained in the class of extending modules, Also we consider the class of strongly quasi-monoform modules, an R-module M is called strongly quasi-monoform if every nonzero proper submodule of M is quasi-invertible relative to some direct summand of M. Conditions are investigated to identify between these classes. Several properties are considered for such modules

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Publication Date
Tue Jan 01 2019
Journal Name
Italian Journal Of Pure And Applied Mathematics
Co-small monoform modules
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he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga

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Publication Date
Tue Jan 01 2013
Journal Name
International Journal Of Algebra
Fully extending modules
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Throughout this paper we introduce the concept of quasi closed submodules which is weaker than the concept of closed submodules. By using this concept we define the class of fully extending modules, where an R-module M is called fully extending if every quasi closed submodule of M is a direct summand.This class of modules is stronger than the class of extending modules. Many results about this concept are given, also many relationships with other related concepts are introduced.

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Publication Date
Thu Oct 16 2014
Journal Name
Journal Of Advances In Mathematics
Strongly Rickart Modules
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Publication Date
Mon Jan 01 2024
Journal Name
Fifth International Conference On Applied Sciences: Icas2023
Ejectivity and goldie-extending modules
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Publication Date
Wed Mar 30 2022
Journal Name
Iraqi Journal Of Science
On Annihilator-Extending Modules
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    Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.

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Publication Date
Wed Sep 01 2021
Journal Name
Baghdad Science Journal
Stable Semisimple Modules, Stable t- Semisimple Modules and Strongly Stable t-Semisimple Modules
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        Throughout this paper, three concepts are introduced namely stable semisimple modules, stable t-semisimple modules and strongly stable t-semisimple. Many features co-related with these concepts are presented. Also many connections between these concepts are given. Moreover several relationships between these classes of modules and other co-related classes and other related concepts are introduced.

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Publication Date
Wed Nov 11 2015
Journal Name
Thesis
St-Closed and Semi-extending Modules
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Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

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Publication Date
Sun Mar 02 2014
Journal Name
Baghdad Science Journal
On Strongly F – Regular Modules and Strongly Pure Intersection Property
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A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .

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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Quasi-Small Prime Modules
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Abstract<p>Let R be a commutative ring with identity, and W be a unital (left) R-module. In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.</p>
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Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
T-Small Quasi-Dedekind modules
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Abstract<p>Let Q be a left Module over a ring with identity ℝ. In this paper, we introduced the concept of T-small Quasi-Dedekind Modules as follows, An R-module Q is T-small quasi-Dedekind Module if, <inline-formula> <tex-math><?CDATA $\forall \,w\,\in En{d}_{R}(Q),\,w\ne 0$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mo>∀</mo> <mspace width="0.25em"></mspace> <mi>w</mi> <mspace width="0.25em"></mspace> <mo></mo></mrow></math></inline-formula></p> ... Show More
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