let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$  is arens regular. we also study the relationship between derivations of $a$ and $e$.

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

the largest class of algebraic hyper structures satisfying the module like axioms is the v h -module. in this paper, we consider the category of v h -modules and prove that the direct limit alwaysexists in this category. direct limits are defined by a universal property, and so are unique. the mostpowerful tool in order to obtain a module from a given v h - module is the quotient out procedure....

Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX Abstract: We present a system, which is based on a new external, polarization-insensitive differential interference contrast (DIC) module, specifically adapted for detecting defects in semiconductor wafers. We obtained defect signal enhancement relative to the s...

A twin-screw granulator (TSG), a promising equipment for continuous high shear wet granulation (HSWG), achieves the desired level of mixing by a combination of the appropriate screw configuration and a suitable set of process settings (e.g. feed rate, screw speed, etc.), thus producing a certain granule size and shape distribution (GSSD). However, the primary sizing and shaping mechanism behind...

The virulent Lactobacillus plantarum myophage LP65 was isolated from industrial meat fermentation. Tail contraction led to reorganization of the tail sheath and the baseplate; a tail tube was extruded. In ultrathin section the phage adsorbed via its baseplate to the exterior of the cell, while the tail tube tunneled through the thick bacterial cell wall. Convoluted membrane structures were indu...

In the present paper for two $mathfrak{A}$-module Banach algebras $A$ and $B$, we investigate relations between $varphi$-$mathfrak{A}$-module approximate amenability of $A$, $psi$-$mathfrak{A}$-module approximate amenability of $B$, and $varphioplus psi$-$mathfrak{A}$-module approximate amenability of $Aoplus B$ ($l^1$-direct sum of $A$ and $B$), where $varphiin$ Hom$_{mathfrak{A}}(A)$ and $psi...

introduction: determination of waves and the pattern of coastal currents is the first step in finding the effective physical factors on marine environments and coastal regions. moreover, wave induced currents play important roles in the determination of geometry and shape of coasts. in this research, patterns of longshore currents are simulated for situations before and after construction of je...