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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
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Semi-Small Compressible Modules and Semi-Small Retractable Modules
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Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .

    In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Semi-Small Compressible Modules and Semi-Small Retractable Modules
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Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

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Publication Date
Sun Jan 01 2023
Journal Name
Aip Conference Proceedings
E-small prime sub-modules and e-small prime modules
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Publication Date
Mon Apr 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Small Monoform Modules
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 Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce the concept small monoform module as a generalization of monoform module. A module M is called small monoform if for each non zero submodule N of M and for each   f ∈ Hom(N,M), f ≠ 0 implies ker f is small submodule in N. We give the fundamental properties of small monoform modules. Also we present some relationships between small monoform modules and some related 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
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
Wed Feb 22 2023
Journal Name
Iraqi Journal Of Science
Small Pointwise M-Projective Modules
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Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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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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Publication Date
Mon Feb 01 2021
Journal Name
Journal Of Physics: Conference Series
Essential T-small quasi-Dedekind modules
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Abstract<p>Let M be an R-module, where R be a commutative; ring with identity. In this paper, we defined a new kind of submodules, namely T-small quasi-Dedekind module(T-small Q-D-M) and essential T-small quasi-Dedekind module(ET-small Q-D-M). Let T be a proper submodule of an R-module M, M is called an (T-small Q-D-M) if, for all f ∊ End(M), f ≠ 0, implies <italic>Kerf</italic> is an T-small submodule of M <italic>(Kerf</italic>«<sub>T</sub> <italic>M)</italic>, if T≠ 0 then T ⊈ <italic>Kerf</italic>. In case <italic>Kerf</italic> is an essential T-small submodule of M <italic>(Kerf <<</italic></p> ... Show More
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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Interdisciplinary Mathematics
Pr-small R-submodules of modules and Pr-radicals
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The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

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