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(θ1,θ2) - Derivation Pair on Rings
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     Ring theory is one of the influential branches of abstract algebra. In this field, many algebraic problems have been considered by mathematical researchers who are working in this field. However, some new concepts have been created and developed to present some algebraic structures with their properties. Rings with derivations have been studied fifty years ago, especially the relationships between the derivations and the structure of a ring. By using the notatin of derivation, many results have been obtained in the literature with different types of derivations. In this paper, the concept of the derivation theory of a ring has been considered. This study presented the definition of

     Ring theory is one of the influential branches of abstract algebra. In this field, many algebraic problems have been considered by mathematical researchers who are working in this field. However, some new concepts have been created and developed to present some algebraic structures with their properties. Rings with derivations have been studied fifty years ago, especially the relationships between the derivations and the structure of a ring. By using the notatin of derivation, many results have been obtained in the literature with different types of derivations. In this paper, the concept of the derivation theory of a ring has been considered. This study presented the definition of (θ1,θ2) derivation pair and Jordan (θ1,θ2)-derivation pair on an associative ring Γ, and the relation between them. Furthermore, we study the concept of prime rings under this notion by introducing some of its properties where θ1  and θ2 are two mappings of Γ into itself.

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Publication Date
Sun Oct 22 2023
Journal Name
Iraqi Journal Of Science
On The Generalized Type and Generalized Lower Type of Entire Function in Several Complex Variables With Index Pair (p, q)
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In the present paper, we will study the generalized ( p, q) -type and
generalized lower ( p, q) -type of an entire function in several complex
variables with respect to the proximate order with index pair ( p, q) are
defined and their coefficient characterizations are obtained.

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Publication Date
Tue Dec 29 2020
Journal Name
Iraqi Journal Of Science
Spectrophotometric Estimation of Losartan Potassium with Methylene Blue by Ion-Pair Extraction Method
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A selective and sensitive spectrophotometric extraction method was established and used to estimate antihypertensive drug, losartan potassium. The method is based on the formation of blue ion pair of the anionic drug, losartan, and the cationic dye, methylene blue, at adjusted pH 6.5 in aqueous solutions, followed by quantitative extraction to dichloromethane;.The observed maximum absorbance was at π 654.9 nm. With 4.53321 x 105 M-1 cm-1 molar absorptivity, Beer's law was obeyed within a concentration range of 0.03-1.5 μg / ml. The limit of detection and the limit of quantification were 0.01μg / ml and 0.03μg / ml, respectively. The method's precision was estimated by a relative standard devi

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Publication Date
Sun Jul 02 2023
Journal Name
Iraqi Journal Of Science
On The Generalized Type and Generalized Lower Type of Entire Function in Several Complex Variables With Index Pair (p, q)
...Show More Authors

In the present paper, we will study the generalized ( p, q) -type and
generalized lower ( p, q) -type of an entire function in several complex
variables with respect to the proximate order with index pair ( p, q) are
defined and their coefficient characterizations are obtained.

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Publication Date
Tue Mar 14 2023
Journal Name
Iraqi Journal Of Science
Characterizing Jordan Higher Centralizers on Triangular Rings through Zero Product
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n this paper , we prove that if T is a 2-torsion free triangular ring and be a family of additive mapping then satisfying is a higher centralizer which is means that is Jordan higher centralizer on 2-torsion free triangular ring if and only if is a higher centralizer and also we prove that if be a family of additive mapping satisfying the relation Σ , Then is a higher centralizer.

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Publication Date
Sun Mar 05 2017
Journal Name
Baghdad Science Journal
Notes on Traces of a Symmetric Generalized (?, ?)-Biderivations and Commutativity in Prime Rings
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Let R be a 2-torision free prime ring and ?, ?? Aut(R). Furthermore, G: R×R?R is a symmetric generalized (?, ?)-Biderivation associated with a nonzero (?, ?)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative

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Publication Date
Thu Dec 29 2016
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Univariate and Simplex Optimization for The Analysis of Diphenhydramine-HCl Through Ion-pair Formation
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    A Simple, rapid and sensitive extractive and spectrophotometric method has been described for the analysis of diphenhyldramine –HCl (DPH) in pure form and in pharmaceutical formulations. The method is based on the formation of chloroform soluble ion-pair  complex with Bromophenol blue(BPB) in a phthalate buffer at pH 3.0.The extracted complex shows maximum absorbance at 410 nm. Beer's law is obeyed in the concentration range 0.2-25.0 µg.ml-1. The molar absorptivity and Sandell's sensitivity for the system being  2.416x104 L.mol-1.cm-1 and 0.012µg.cm-2, respectively. The limit of detection was found to be 0.155 µg.ml-1.           The proposed me

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Publication Date
Wed Jun 01 2016
Journal Name
Journal Of The College Of Basic Education
Spectrophotometric determination of ciprofloxacin by Ion pair complex formation with bromothymol blue‏
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Publication Date
Fri Sep 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Spectrophotometric Determination of Chlorpromazine -HCI by Ion -Pair Complex Formation with Acid Dyes
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A simple, rapid, accurate and sensitive spectrophotometric method is  proposed  for  the  detennination  of chlorprQm<tZine -HCl  in  pwe form  and  in pharmaceutical  formulation. This method is based on the formation.  of ion  assodation complexes  of  dmg   with either  thymol

blue or  bromophenol  blue  in an acidic buffer at pH  values 4.17  and

3.68, respectively.

The ion-pair  complexes  formed exhibit absorption maxima  at 41 Onm for  both  thymol   blue and  bromophenol  blue.  These  complexes· are quantitatively extracted  &n

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Publication Date
Sun Jun 30 2024
Journal Name
Malaysian Journal Of Science
SIMPLEX OPTIMIZATION FOR THE SPECTROPHOTOMETRIC DETERMINATION OF AZITHROMYCIN DRUG VIA ION-PAIR FORMATION
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A spectrophotometric determination of azithromycin was optimized using the simplex model. The approach has been proven to be accurate and sensitive. The analyte has been reacted with bromothymol blue (BTB) to form a colored ion pair which has been extracted in chloroform in a buffer medium of pH=4 of potassium phthalate. The extracted colored product was assayed at 415 nm and exhibited a linear quantification range over (1 - 20) g/ml. The excipients did not exhibit any interferences with the proposed approach for assaying azithromycin in pharmaceutical formulations.

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Scopus
Publication Date
Tue Nov 30 2021
Journal Name
Iraqi Journal Of Science
Some Generalizations of Semisimple Gamma Rings
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In this paper we introduce and study the concepts of semisimple gamma modules , regular gamma modules and fully idempotent gamma modules as a generalization of semisimple ring. An module is called fully idempotent (semisimple , regular) if for all submodule of (every submodule is a direct summand, for each , there exists and such that . We study some properties and relationships between them.

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