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...

X iv :0 80 1. 22 07 v1 [ m at h. R A ] 1 5 Ja n 20 08 The derivation algebra and automorphism group of the twisted Schrödinger-Virasoro algebra Junbo Li, Yucai Su ∗)Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China †)Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China ‡)Department of Mathematics, University of Science and Technology...

When an algebra is graded by a group, any additive character of the group induces a diagonalizable derivation of the ring. This construction is studied in detail for the case of a path algebra modulo relations and its fundamental group. We describe an injection of the character group into the first cohomology group following Assem-de la Peña. Rather general conditions are determined, in this co...

Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using this polynomial we define the characteristic polynomial of a multiarrangement which generalizes the characteristic polynomial of an arragnement. The characteristic polynomial of an arrangement is a combinatori...

in this paper we introduce a generalization of m-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . we will use the structure of the radical of a module in  and get some suitable results about this class of modules. also the relation between injective hull in  and this kind of modules will be investigated in this article.   for a module  we show...

This paper describes the system SYNHESYS, which is a shell for developing expert systems composed of both a connectionist module and a symbolic module. The shell allows for several types of interactions between the two modules, and for several degrees of coupling. SYNHESYS aims at facilitating the process of knowledge acquisition and at improving the performance of the symbolic module. We prese...

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,Rin K(H).

Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(...