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....

Modules (also known as profunctors or distributors) and morphisms among them subsume categories and functors and provide more general and abstract framework to explore the theory of structures. In this book we generalize and redevelop the basic notions and results of category theory using this framework of modules. Topics Chapter 1 introduces modules and cells among them. A moduleM ∶ X⇢A from a...

A micro burette, micro pipette, and methods for their use in quantitative toxicological investigations on mandibulate insects are described. It is suggested that the form of curves relating speed of toxic action to dosage may be explained by postulating suitable changes in rate of distribution, excretion, and cell penetration of poison as dosage varies. The speed of toxic action of pentavalent ...

Due to the flexibility and ease of control, unmanned aerial vehicles (UAVs) have been increasingly used in various scenarios applications recent years. Training UAVs with reinforcement learning (RL) for a specific task is often expensive terms time computation. However, it known that main effort process made fit low-level physical dynamics systems instead high-level itself. In this paper, we st...

In past few years, automatic irrigation system has seen a rapid growth in terms of technology. At present cost-saving technology, labor-saving are the addressing key issues in irrigation. This paper gives a review of these systems based on existing technologies and also proposes an economical and generic automatic irrigation system based on wireless sensors with GSM-Bluetooth for irrigation sys...

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...