Let $R$ be a commutative ring with identity and $M$ be an$R$-module. Let $FSpec(M)$ denotes the collection of all prime fuzzysubmodules of $M$. In this regards some basic properties of Zariskitopology on $FSpec(M)$ are investigated. In particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$FSpec(M)$ is a $T_0-$spa...

and Applied Analysis 3 Let L2 Λ be a square integrable function space with inner product and norm as follows:

In this paper, we designed a new detecting system of bridge cables with a snake-shaped robot. It can solve the problems such as inefficiency and danger of aloft work in the bridge detecting by workers. The detecting system of the bridge cables includes: a snake-shaped robot; a multiple and monocular vision detection module; a nondestructive magnetic leakage detecting module; a magnetostrictive ...

$R$-module. In this paper, we explore more properties of $Max$-injective modules and we study some conditions under which the maximal spectrum of $M$ is a $Max$-spectral space for its Zariski topology.

Let g be a simple finite-dimensional Lie algebra and ĝκ, where κ is an invariant inner product on g, the corresponding affine Kac-Moody algebra. Consider the vacuum module Vκ over ĝκ (see Section 2 for the precise definitions). According to the results of [FF, Fr], the algebra of endomorphisms of Vκ is trivial, i.e., isomorphic to C, unless κ = κc, the critical value. The algebra Endĝκc Vκc is ...

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...

Associated to each irreducible crystallographic root system Φ, there is a certain cell complex structure on the torus obtained as the quotient of the ambient space by the coroot lattice of Φ. This is the Steinberg torus. A main goal of this paper is to exhibit a module structure on (the set of faces of) this complex over the (set of faces of the) Coxeter complex of Φ. The latter is a monoid und...