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jih-3089
P-small Compressible Modules and P-small Retractable Modules
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Let  be a commutative ring with 1 and  be left unitary  . In this papers we introduced and studied concept P-small compressible  (An     is said to be P-small compressible if  can be embedded in every of it is nonzero P-small submodule of . Equivalently,  is P-small compressible if there exists a monomorphism  , ,     is said to be P-small retractable if  , for every non-zero P-small submodule of . Equivalently,  is P-small retractable if there exists a homomorphism  whenever  as a generalization of compressible  and retractable  respectively and give some of their advantages characterizations and examples.

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Publication Date
Tue Mar 14 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On e-Small Submodules
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Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

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Publication Date
Sun May 01 2022
Journal Name
Journal Of Physics: Conference Series
D_j -Supplemented Modules
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Scopus
Publication Date
Sun Dec 02 2012
Journal Name
Baghdad Science Journal
Semi – Bounded Modules
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Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

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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 Sep 03 2017
Journal Name
Baghdad Science Journal
CL-duo modules
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In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.

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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 Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
⊕-Rad -supplemented modules
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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
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
⊕-J-supplemented modules
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Scopus
Publication Date
Sun Mar 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
2-Regular Modules
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  In this paper we introduced the concept of 2-pure submodules as a generalization of pure submodules, we study some of its basic properties and by using this concept we define the class of 2-regular modules, where an R-module M is called 2-regular module if every submodule is 2-pure submodule. Many results about this concept are given. 

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