Characterization of $delta$-double derivations on rings and algebras

Characterization of $(delta‎, ‎varepsilon)$-double derivation on rings ‎and ‎algebras

This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...

Derivations in semiprime rings and Banach algebras

Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

Lie $^*$-double derivations on Lie $C^*$-algebras

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

δ-Double Derivations on C*-Algebras

Double derivations of n-Lie algebras

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...