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Pr-small R-submodules of modules and Pr-radicals

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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Publication Date
Fri Jun 30 2023
Journal Name
Iraqi Journal Of Science
Z-Small Quasi-Dedekind Modules

     In this paper, we define and study z-small quasi-Dedekind as a generalization of small quasi-Dedekind modules. A submodule  of -module  is called z-small (  if whenever  , then . Also,  is called a z-small quasi-Dedekind module if for all  implies  . We also describe some of their properties and characterizations. Finally, some examples are given.

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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Quasi-Small Prime Modules
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
Sun Mar 04 2018
Journal Name
Iraqi Journal Of Science
Fully Small Dual Stable Modules

New types of modules named Fully Small Dual Stable Modules and Principally Small Dual Stable are studied and investigated. Both concepts are generalizations of Fully Dual Stable Modules and Principally Dual Stable Modules respectively. Our new concepts coincide when the module is Small Quasi-Projective, and by considering other kind of conditions. Characterizations and relations of these concepts and the concept of Small Duo Modules are investigated, where every fully small dual stable R-module M is small duo and the same for principally small dual stable.

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Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
T-Small Quasi-Dedekind modules
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
Wed Feb 22 2023
Journal Name
Iraqi Journal Of Science
Small Pointwise M-Projective Modules

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
Tue Feb 13 2024
Journal Name
Iraqi Journal Of Science
On δ-Small Projective Modules

Let be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.

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Publication Date
Sun Mar 04 2018
Journal Name
Iraqi Journal Of Science
Essential-Small M-Projective Modules

In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.

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Publication Date
Sun May 17 2020
Journal Name
Iraqi Journal Of Science
Relationship of Essentially Small Quasi-Dedekind Modules with Scalar and Multiplication Modules

Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.

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Publication Date
Sun Oct 02 2016
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Evaluation of triple hormonal content (ER, PR, and HER\2neu)of breast cancer specimens obtained from breast cancer patients using tru-cut biopsy

Background: Breast cancer is the commonest type of malignancy among women worldwide and in Iraq. Tru-cut needle biopsy technique provides adequate tissue for histopathological diagnosis of suspected breast lumps and assessment of hormonal receptors (estrogen, progesterone and HER2neu) prior to surgical operation.
Objectives: To assess estrogen, progesterone andHER2neu expression using breast cancer tissue specimens obtained by tru-cut biopsy, to correlate the findings with clinicopathological parameters of known prognostic significance in breast cancer patients.
Patients and Methods: This prospective study was held within the Main Referral Center for Early Detection of Breast Tumors/Medical City Teachi

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Publication Date
Mon Feb 01 2021
Journal Name
Journal Of Physics: Conference Series
Essential T-small quasi-Dedekind modules
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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