Abstract In this work we introduce the concept of approximately regular ring as generalizations of regular ring, and the sense of a Z- approximately regular module as generalizations of Z- regular module. We give many result about this concept.
Let R be a commutative ring with identity . In this paper we study the concepts of essentially quasi-invertible submodules and essentially quasi-Dedekind modules as a generalization of quasi-invertible submodules and quasi-Dedekind modules . Among the results that we obtain is the following : M is an essentially quasi-Dedekind module if and only if M is aK-nonsingular module,where a module M is K-nonsingular if, for each , Kerf ≤e M implies f = 0 .
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Let M is a Г-ring. In this paper the concept of orthogonal symmetric higher bi-derivations on semiprime Г-ring is presented and studied and the relations of two symmetric higher bi-derivations on Г-ring are introduced.
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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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Schiff bases (Sh1-Sh3) have been synthesized (p-aminophenol) was condensed with different aromatic aldehyde in ethanol inthe presence of glacial acetic acid as catalyst. These Schiff bases on treatment with monochloroacetyl choride gave 3-chloro-1-(4-hydroxyphenyl)-4-(substituted)azetidin-2-one(Az4-Az6), with αmercaptoacetic acid gave 3-(4-hydroxyphenyl)-2-( substituted)thiazolidin-4-one (Th7-Th9) and with anthranilic acid gave 3-(4-hydroxyphenyl)-2(substituted)-2,3-dihydroquinazolin-4(1H)-one (Qu10-Qu12). The purity of the derivatives was confirmed by TLC. The some compoundsidentify by (FT-IR and1H, 13C-NMR) data. Some of derivatives were evaluated activity against several microbesto determine ability to inhibit bacterial in some h
... Show MoreVarious types of heterocyclic seven membered rings were prepared from the reaction of 2,3Pyridine caroboxylic anhydride with Schiff bases (which was prepared using different Aldehydes with amines [H1-H10] and seven membered rings were prepared (derivatives of 7,8-dihydropyrido[2,3e][1,3]oxazepine-5,9-dione, and the presence of Aceton. [A1-A10]. Melting points of the compounds were measured. The prepared compounds were diagnosed spectrally by using UV-Visible and Infrared spectroscopy, and (1H-NMR) Spectrum for some compounds. The results confirmed the validity of the proposed chemical compositions.
In this paper, we study a new concept of fuzzy sub-module, called fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense. This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.
Let M be an R-module, where R is commutative ring with unity. In this paper we study the behavior of strongly hollow and quasi hollow submodule in the class of strongly comultiplication modules. Beside this we give the relationships between strongly hollow and quasi hollow submodules with V-coprime, coprime, bi-hollow submodules.
Frustrated Total Internal Reflection FTIR phenomenon is manifested employing Newton‟s rings setup generated via a coherent light beam of a laser diode ( . All concentric bright and dark rings, except the central bright spot, were noticed to recede (disappear) when the incident angle exceeded the critical angle of 41o.
It was also shown that the current setup has proven its applicability for other tests and can give convenient results that conform with theory. Neither the concept nor the design is beyond what can be realized in an undergraduate laboratory. However, technical improvements in mounting the prism - lens may be advisable. As an extension of the experiments, the effect can be studied using hollow prism filled with liquids