E-small prime sub-modules and e-small prime modules
Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
J-semi regular modules
Abstract<p>Let <italic>R</italic> be a ring with identity and let <italic>M</italic> be a left R-module. <italic>M</italic> is called J-semiregular module if every cyclic submodule of <italic>M</italic> is J-lying over a projective summand of <italic>M</italic>, The aim of this paper is to introduce properties of J-semiregular module Especially, we give characterizations of J-semiregular module. On the other hand, the notion of J-semi hollow modules is studied as a generalization of semi hollow modules, finally <italic>F</italic>-J-semiregular modules is studied as a generalization of <italic>F</italic>-semiregular modules.</p>
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Publication Date
Sun Mar 01 2020
Journal Name
Baghdad Science Journal
On S*-Supplemented Modules
-hollow
-small submodule
d*- supplement
d*- supplemented
W-supplemented
The main goal of this paper is to introduce and study a new concept named d*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d*-supplement submodule. Many relationships of d*-supplemented modules are studied. Especially, we give characterizations of d*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d*-supplemented and by an example we show that the converse is not true.
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Publication Date
Sun Dec 05 2010
Journal Name
Baghdad Science Journal
ON M- Hollow modules
"Maximal Submodule
Small Submodule
Hallow Module
Projective Module and Lifting Module"
Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.
Publication Date
Sun Sep 04 2011
Journal Name
Baghdad Science Journal
On Primary Multipliction Modules
Multiplication module
Weak multiplication
Primary submodule
Primary multiplication module.
Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.
Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
On J–Lifting Modules
Abstract<p>Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if for every submodule N of M, there exists a submodule K of N such that <inline-formula>
<tex-math><?CDATA ${\rm{M}} = {\rm{K}} \oplus \mathop {\rm{K}}\limits^\prime,\>\mathop {\rm{K}}\limits^\prime \subseteq {\rm{M}}$?></tex-math>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll">
<mrow>
<mi mathvariant="normal">M</mi>
<mo>=</mo>
<mi mathvariant="normal">K</mi></mrow></math></inline-formula></p>
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Publication Date
Sun Mar 01 2020
Journal Name
Baghdad Science Journal
On S*-Supplemented Modules
-hollow
-small submodule
*- supplement
*- supplemented
W-supplemented
The main goal of this paper is to introduce and studya new concept named Ᵹ*-supplemented which can be considered as a generalization of W-supplemented modules and Ᵹ-hollow module. Also, we introduce a Ᵹ*-supplement submodule.Many relationshipsof Ᵹ*-supplemented modules are studied. Especially, we give characterizations of Ᵹ*-supplemented modules and relationship between this kind of modules and other kind modules for example every Ᵹ-hollow (Ᵹ-local) module is Ᵹ*-supplemented and by an example we show that the converse is not true.
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Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
J-Small Semiprime Submodules
Abstract<p>Let <italic>R</italic> be a commutative ring with identity and <italic>Y</italic> be an unitary <italic>R</italic>-module. We say a non-zero submodule <italic>s</italic> of <italic>Y</italic> is a <italic>J –</italic> small semiprime if and only if for whenever <italic>i</italic> ∈ <italic>R, y ∈ Y,(Y)</italic> is small in <italic>Y</italic> and <italic>i<sup>2</sup>y</italic> ∈ <italic>S</italic> + <italic>Rad (Y)</italic> implies <italic>iy</italic> ∈ <italic>S.</italic> In this paper, we investigate some properties and chara</p>
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Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Weakly Small Smiprime Submodules
Abstract<p>Let <italic>R</italic> be a commutative ring with an identity, and <italic>G</italic> be a unitary left <italic>R</italic>-module. A proper submodule <italic>H</italic> of an <italic>R</italic>-module <italic>G</italic> is called semiprime if whenever <italic>a ∈ R, y ∈ G, n ∈ Z</italic>
<sup>+</sup> and <italic>a<sup>n</sup>y ∈ H</italic>, then <italic>ay ∈ H</italic>. We say that a properi submodule <italic>H</italic> of an <italic>R</italic>-module <italic>G</italic> is a weakly small semiprime, if whenever <ita></ita></p>
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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Small Semiprime Submodules
Abstract<p>Let R be a commutative ring with identity, and M be unital (left) R-module. In this paper we introduce and study the concept of small semiprime submodules as a generalization of semiprime submodules. We investigate some basis properties of small semiprime submodules and give some characterizations of them, especially for (finitely generated faithful) multiplication modules.</p>
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Publication Date
Thu Sep 13 2018
Journal Name
Baghdad Science Journal
St-Polyform Modules and Related Concepts
?-nonsingular modules
Polyform modules
Semi-essential submodules
St-closed submodules
Strongly essentially quasi-Dedekind modules.
In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and ?-nonsingular modules. Various properties of such modules are obtained. Another characterization of St-polyform module is given. An existence of St-polyform submodules in certain class of modules is considered. The relationships of St-polyform with some related concepts are investigated. Furthermore, we introduce other new classes which are; St-semisimple and ?-non St-singular modules, and we verify that the class of St-polyform modules lies between them.
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