One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous Hochschild cohomology for operator algebras R. V. Kadison and J. R. Ringrose proved [10] that for any hyperfinite von Neumann algebra M and any dual normal M-bimodule S, all the continuous cohomology gro...

We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on...

We give an algorithm of decomposition for a finite-dimensional Lie algebra over a field of characteristic 0 permitting to generalize the derivation tower theorem of Lie algebras.

LetN be a zero-symmetric left near-ring, not necessarily with amultiplicative identity element; and letZ be its multiplicative center. DefineN to be 3-prime if for all a, b ∈ N\{0}, aNb / {0}; and callN 2-torsion-free if N, has no elements of order 2. A derivation onN is an additive endomorphism D of N such that D xy xD y D x y for all x, y ∈ N. A generalized derivation f with associated deriva...

Let M be a 2-torsion free prime Γ-ring and X a nonzero faithful and prime ΓM -module. Then the existence of a nonzero Jordan left derivation d : M → X satisfying some appropriate conditions implies M is commutative. M is also commutative in the case that d : M → M is a derivation along with some suitable assumptions. AMS (MOS) Subject Classification Codes: 03E72, 54A40, 54B15

Based on a description of the squares of cofinite primary ideals of A + α (D), we prove the following results: for α ≥ 1, there exists a derivation from A + α (D) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m ∈ N and α ∈ [m, m + 1), every finite-dimensional extension of A + α (D) splits algebraically if and only if α ≥ m + 1/2.

Let V be an l-dimensional Euclidean space. Let G ⊂ O(V ) be a finite irreducible orthogonal 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). For each nonnegative integer m, define the derivation module D(A) = {θ ∈ DerS | θ(αH) ∈ SαmH}. The module is known to be a free S-module of...

Following the recent work by Chan [4] and Morton and Hadji [7] on the Homflypt polynomials of some generalized Hopf links, we investigate the Kauffman polynomials of generalized Hopf links. By studying the Kauffman skein module of the solid torus S × D, we establish a similar skein map on the Kauffman skein module of S × D which has distinct eigenvalues. Furthermore we are able to calculate the...

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that such a generalized weight module is simply a module obtained by “linking” sub-quotient modules of generalized Kac-modules. By applying our results to sl(m/1), ...