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This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-1...
Abstract: Let $A$ be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of $A$ with coefficients in the bimodule $A$ vanishes if and only...
Abstract: We defined \delta-derivations of n-ary algebras. We described \delta-derivations of (n+1)-dimensional n-ary Filippov algebras and simple finite-dimensional Filippov algebras over algebraical...
Abstract: We defined generalized \delta-derivations of algebra A as linear mapping \chi associated with usual \delta-derivation \phi by the rule \chi(xy)=\delta(\chi(x)y+x\phi(y))=\delta(\phi(x)y+x\ch...
Abstract: Kramers' law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. We review different approaches that have been followed to ob...
Abstract: We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial...
Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for...
We consider a Weitzenb\"ock derivation $\Delta$ acting on a polynomial ring $R=K[\xi_1,\xi_2,...,\xi_m]$ over a field $K$ of characteristic 0. The $K$-algebra $R^\Delta = \{h \in R \mid \Delta(h) = 0...
A Note on Derivations of Lie Algebras     Note  Lie Algebras       2010/11/12
In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D...
We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of ( , )-derivation to ( , )-higher derivation and demonstrate that a filter of a...
We consider a circle of ideas involving differential algebra, local Noetherian rings, and their generic formal fibers. Connecting these ideas gives rise to what we term a “twisted” subring R of a ring...
In this paper, we introduce and discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module.
A general hydrodynamic solution is derived for arbitrary gravity-wave fields on the ocean surface by extending Stokes' (1847) original perturbational analysis. The solution to the nonlinear equations ...
Let \A be a unital Banach algebra and let m, 1 \leq m \leq 4, be an integer. If f: \A \to \A is an approximate m-order derivation in the sense of Hyers-Ulam-Rassias, then f: \A \to \A is an exact m-or...
设$R$是2-扭自由的素环,$Z$是它的中心,$U$是它的Lie理想.如果$d$是$R$的一个导子,并且在$U$上是同态或反同态,则$d=0$,或者$U\subseteq Z$.此结果改进了Asma, Rehman,以及Shakir的一个定理.

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