Let R be a Γ-ring and G be an R_Γ-module. A proper R_Γ-submodule S of G is said to be semiprime R_Γ-submodule if for any ideal I of a Γ-ring R and for any R_Γ-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime R_Γ-submodule of R_Γ-module which represents a generalization of semiprime submodules.

        Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.

A rapid and sensitive method for the determination of amoxicillin trihydrate (AMXT) based on the diazo-coupling reaction was studied. Sulphanilic acid diazotizes with nitrite ion in acidic medium to produce a water soluble, colorless diazonium ion, which subsequently coupled with AMXT to form a colored azo dye in the alkaline medium, having maximum absorption at 455 nm. The calibration graph showed that Beer's law is obeyed over the concentration range of 0.3 – 30.0 μg/mL of AMXT, with the detection limit of 0.15 μg/mL and molar absorptivity was 2.3 × 104 L/mol.cm. The accuracy and the precision were acceptable depending upon the values of error percentage and relative standard deviation. The influence of common interfer

In this paper, we present the almost approximately nearly quasi compactly packed (submodules) modules as an application of the almost approximately nearly quasiprime submodule. We give some examples, remarks, and properties of this concept. Also, as the strong form of this concept, we introduce the strongly, almost approximately nearly quasi compactly packed (submodules) modules. Moreover, we present the definitions of almost approximately nearly quasiprime radical submodules and almost approximately nearly quasiprime radical submodules and give some basic properties of these concepts that will be needed in section four of this research. We study these two concepts extensively.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Practically, torsion is normally combined with flexure and shear actions. Even though, the behavior of reinforced concrete continuous beams under pure torsion is investigated in this study. It was performed on four RC continuous beams under pure torsion. In order to produce torsional moment on the external supports, an eccentric load was applied at various distances from the longitudinal axis of the RC beams until failure.

Variables considered in this study are absolute vertical displacement of the external supports, torsional moment’s capacity, angle of twist and first cracks occurrences. According to experimental results; when load eccentricity increased from 30cm to 60cm, the absolute vertical displacement i

     Let R be a commutative ring with 1 and M be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) Modules. We study s-essentially compressible (s-essentially retractable). We give some of their advantages, properties, characterizations and examples. We also study the relation between s-essentially compressible   (s-essentially retractable modules) and some classes of modules.

  Let L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called  s- closed submodule denoted by  D ≤sc W, if D has   no  proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In  this  paper,  we study  modules which satisfies  the ascending chain  conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.