We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of (α, β)-derivation to (α, β)higher derivation and demonstrate that a filter of a hereditary torsion theory that is invariant for α and β is (α, β)-higher derivation invariant. As a consequence, any higher derivation can be extended from a module to its module of quotients. Then...

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...

Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove th...

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert C∗-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert C∗-module M over a C∗-algebra A as a oneparameter group of unitaries on M and prove that if α : R → U(M) is a dynamical system, where U(M) denotes the set of all unitary operator on M, th...

Let V be Euclidean space. Let W ⊂ GL(V ) be a finite irreducible reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H ∈ A choose αH ∈ V ∗ such that H = ker(αH). The arrangement A is known to be free: the derivation module D(A) = {θ ∈ DerS | θ(αH ) ∈ SαH} is a free S-module with generators of degrees equal to the exponents of ...

Abstract The system presented in this paper is concerned with the computational processing of the selected types of Czech word-formation. The developed programming tool (word-formation module) aims at analysing and synthesising Czech derived words. Such a system is of particular value for automatic processing of Czech language where derivational morphology plays an important role in regular wor...

Due to the special requirements of distributed systems, it is important that modeling techniques for this kind of systems ooer a stringent module concept. Each module has to support the encapsulation of data structure as well as functionality also at runtime. Modular graph transformation, presented in this contribution, supports these features. Modules are built up of speciications where attrib...