The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this concept and it is relationship to previous generalizationsm especially 2-Absorbing submodule and Quasi-2-Absorbing submodule, in addition to studying the most important Propositions, charactarizations and Examples. Now in this research, which is considered a continuation of the definition that was presented earlier, which is the Extend Nearly Pseudo Quasi-2-Absorbing submodules, we have completed the study of this concept in multiplication modules. And the relationship between the Extend Nearly Pseudo Quasi-2-Absorbing submodule and Extend Nearly Pseudo Quasi-2-Absorbing ideal. We also studied more result of Extend Nearly Pseudo Quasi-2-Absorbing submodule in multiplication module. In the end, we obtained new Propositions and distinguished results in studying this concept.
This work describes the synthesis of novel ligand (H2L2) (4-((2-hydroxy-5-nitrophenyl)imino)methyl)-5(hydroxymethyl)-2methylpyridin-3-ol) type (NOO) donor atoms. When it coordinates with metal ions[V2+,Mn2+,Fe2+,Co2+,Ni2+,Cu2+and Pt4+] with the general formula K2[M(L2)2].XH2O and K2[VO(L2)(OSO3)].H2O . This ligand can form tridentate structures. The ligand was synthesized from the reaction of pyridoxal hydrochloride with 2-amino-4-nitrophenol in ethanol (as a solvent) at a mole ratio of 1:1 and thoroughly mixed and refluxed for 6-8 hrs . The reaction
... Show MoreThe duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl
... Show More"In this article, "we introduce the concept of a WE-Prime submodule", as a stronger form of a weakly prime submodule". "And as a "generalization of WE-Prime submodule", we introduce the concept of WE-Semi-Prime submodule, which is also a stronger form of a weakly semi-prime submodule". "Various basic properties of these two concepts are discussed. Furthermore, the relationships between "WE-Prime submodules and weakly prime submodules" and studied". "On the other hand the relation between "WE-Prime submodules and WE-Semi-Prime submodules" are consider". "Also" the relation of "WE-Sime-Prime submodules and weakly semi-prime submodules" are explained. Behind that, some characterizations of these concepts are investigated".
... Show MoreLet R be a Γ-ring and G be an RΓ-module. A proper RΓ-submodule S of G is said to be semiprime RΓ-submodule if for any ideal I of a Γ-ring R and for any RΓ-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime RΓ-submodule of RΓ-module which represents a generalization of semiprime submodules.
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.
Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXïƒW for all fully invariant R-submodule X of M, implies XïƒW. M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.
In this work, the notion of principally quasi- injective semimodule is introduced, discussing the conditions needed to get properties and characterizations similar or related to the case in modules.
Let be an -semimodule with endomorphism semiring Ș. The semimodule is called principally quasi-injective, if every -homomorphism from any cyclic subsemimodule of to can be extended to an endomorphism of .
Let R be a commutative ring , the pseudo – von neuman regular graph of the ring R is define as a graph whose vertex set consists of all elements of R and any two distinct vertices a and b are adjacent if and only if , this graph denoted by P-VG(R) , in this work we got some new results a bout chromatic number of P-VG(R).
We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module over a commutative ring with identity as a generalization of a prime submodules and semi-prime submodules, also generalization of quasi-prime submodules and approximaitly prime submodules. Various basic properties of an approximaitly semi-prime submodules are discussed, where a proper submodule of an -module is called an approximaitly semi-prime submodule of , if whenever , where , and , implies that . Furthermore the behaviors of approximaitly semi-prime submodule in some classes of modules are studied. On the other hand several characterizations of this concept are
... Show MoreA simple ,accurate and sensitive spectrophotometric method has been developed the determination of Cobalt(II) and Cupper (II) .The method is based on the chelation of Co(II) and Cu(II) ions with 4-(4´-pyrazolon azo) -2-Naphthol(APAN) in aqueous medium . The complexes have a maximum absorption at (513) and (506) nm and ? max 0.531×10 4 and 0.12×10 5 L.mol -1.cm -1 for Co(II) and Cu(II) respectively .The reagent and two complexes have been prepared in ethanolic solution.The stoichiometry of both complexes were found to be 1:2 (metal :legend) .The effects of various cations and anions on Co(II) and Cu(II) determination have been investigated .The stability constants and standard deviations for Co(II) and Cu(II) 0.291 x107 ,0.909X108 L.mol
... Show More