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ESSENTIAL T-hollow-lifting module
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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-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012070_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> is <inline-formula> <tex-math><?CDATA $E(\frac{T+H}{H})$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>E</mi> <mo stretchy="false">(</mo> <mfrac> <mrow> <mi>T</mi> <mo>+</mo> <mi>H</mi> </mrow> <mi>H</mi> </mfrac> <mo stretchy="false">)</mo> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012070_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>-hollow, then there exists a direct summand D of M such that <inline-formula> <tex-math><?CDATA $D\subseteq E(\frac{T+D}{D})ce$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>D</mi> <mo>⊆</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mfrac> <mrow> <mi>T</mi> <mo>+</mo> <mi>D</mi> </mrow> <mi>D</mi> </mfrac> <mo stretchy="false">)</mo> <mi>c</mi> <mi>e</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012070_ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula>. we introduce some properties of ET-hollow lifting module.</p>
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Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
On µ-Semiregular Module
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Abstract<p>Let R be an associative ring with identity and let M be right R-module M is called μ-semi hollow module if every finitely generated submodule of M is μ-small submodule of M The purpose of this paper is to give some properties of μ-semi hollow module. Also, we gives conditions under, which the direct sum of μ-semi hollow modules is μ-semi hollow. An R-module is said has a projective μ-cover if there exists an epimorphism <italic>f</italic>:P→M Where P is a projective R-module and ker (<italic>f</italic>)<sub>≪</sub> P.And study some properties of Projective μ-cover of M. Were studied Moreover, An module M is μ-semiregular module if every cyclic</p> ... Show More
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Publication Date
Fri Jan 26 2024
Journal Name
Iraqi Journal Of Science
Fully Principally Extending Module
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In this work, We introduce the concepts of an FP-Extending, FP-Continuous and FP-Quasi-Continuous which are stronger than P-Extending, P-Continuous and P-Quasi-Continuous. characterizations and properties of FP-Extending, FP-Continuous and FP-Quasi-Continuous are obtained . A module M is called FP-Extending ( FP-Continuous, FP-Quasi-Continuous) if every submodule is P-Extending (P-Continuous, P-Quasi-Continuous) .

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Publication Date
Fri Jan 01 2010
Journal Name
Iraqi Journal Of Science
PRIME HOLLOW MODULES
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A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.

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Publication Date
Mon Apr 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
δ-Hollow Modules
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    Let R be a commutative ring with unity and M be a non zero unitary left R-module. M is called a hollow module if every proper submodule N of M is small (N ≪ M), i.e. N + W ≠ M for every proper submodule W in M. A δ-hollow module is a generalization of hollow module, where an R-module M is called δ-hollow module if every proper submodule N of M is δ-small (N δ  M), i.e. N + W ≠ M for every proper submodule W in M with M W is singular. In this work we study this class of modules and give several fundamental properties related with this concept

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Publication Date
Sun Jan 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
T-ABSO T-Abso and T-Abso Quasi Primary Fuzzy Submodules
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     Let Ḿ be a unitary R-module and R is a commutative ring with identity. Our aim in this paper  to study the concepts T-ABSO fuzzy ideals, T-ABSO fuzzy submodules and T-ABSO quasi primary fuzzy submodules, also we discuss these concepts in the class of multiplication fuzzy modules and relationships between these concepts. Many new basic properties and characterizations on these concepts are given.

 

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Publication Date
Thu May 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On Weakly Quasi-Prime Module
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  In this work we shall introduce the concept of weakly quasi-prime modules and give some properties of this type of modules.

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Publication Date
Sun Dec 05 2010
Journal Name
Baghdad Science Journal
ON M- Hollow modules
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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.

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Publication Date
Sat Apr 30 2022
Journal Name
Iraqi Journal Of Science
On Large-Lifting and Large-Supplemented Modules
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      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

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Publication Date
Sat Apr 30 2022
Journal Name
Iraqi Journal Of Science
On Large-Lifting and Large-Supplemented Modules
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      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

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Publication Date
Thu May 04 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Strongly (Comletely) Hollow Submodules I
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Let R be a commutative ring with unity and let M be an R-module. In this paper we
study strongly (completely) hollow submodules and quasi-hollow submodules. We investigate
the basic properties of these submodules and the relationships between them. Also we study
the be behavior of these submodules under certain class of modules such as compultiplication,
distributive, multiplication and scalar modules. In part II we shall continue the study of these
submodules.

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