e*-Essential small submodules and e*-hollow module
Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
ESSENTIAL T-hollow-lifting module
Abstract<p>Let M be a R-module, where R be a commutative ring with identity, In this paper, we defined a new kind of module namely ET-hollow lifting module, Let T be a submodule of M, M is called ET-hollow lifting module if for every sub-module H of M with <inline-formula>
<tex-math><?CDATA $\frac{M}{H}$?></tex-math>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mrow>
<mfrac>
<mi>M</mi>
<mi>H</mi>
</mfrac>
</mrow>
</math></inline-formula></p>
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Publication Date
Tue Nov 30 2021
Journal Name
Journal Of The Indonesian Mathematical Society
Publication Date
Sun Jan 01 2023
Journal Name
Aip Conference Proceedings
Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Large-Small submodule and Large-Hollow module
Abstract<p>The goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤<sub>e</sub> M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.</p>
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Publication Date
Sun Mar 01 2009
Journal Name
Baghdad Science Journal
Weak Essential Submodules
Semi-prime submodules
Essential submodules
Uniform modules.
A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.
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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
Annihilator Essential Submodules
Abstract<p>Through this paper R represent a commutative ring with identity and all R-modules are unitary left R-modules. In this work we consider a generalization of the class of essential submodules namely annihilator essential submodules. We study the relation between the submodule and his annihilator and we give some basic properties. Also we introduce the concept of annihilator uniform modules and annihilator maximal submodules.</p>
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Publication Date
Wed Jun 26 2019
Journal Name
Iraqi Journal Of Science
H-essential Submodules and Homessential Modules
Essential submodules
H-essential submodules
Homessential modules
The main goal of this paper is introducing and studying a new concept, which is named H-essential submodules, and we use it to construct another concept called Homessential modules. Several fundamental properties of these concepts are investigated, and other characterizations for each one of them is given. Moreover, many relationships of Homessential modules with other related concepts are studied such as Quasi-Dedekind, Uniform, Prime and Extending modules.
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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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