A note on derivations with power central values on a Lie ideal
نویسندگان
چکیده
منابع مشابه
Commutators with Power Central Values on a Lie Ideal
Theorem ([11, Theorem 2, page 282]). Let R be a prime ring, L a noncommutative Lie ideal of R and d 6= 0 a derivation of R. If [d(x), x] ∈ Z(R), for all x ∈ L, then either R is commutative, or char(R) = 2 and R satisfies s4, the standard identity in 4 variables. Here we will examine what happens in case [d(x), x]n ∈ Z(R), for any x ∈ L, a noncommutative Lie ideal of R and n ≥ 1 a fixed integer....
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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.
15 صفحه اولderivations with power values on multilinear polynomials
a polynomial 1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let r be a prime k-algebra over a commutative ring k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that d is a nonzero derivation on r such that ...
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In a recent paper Borel and Serre proved the theorem: If 8 is a Lie algebra of characteristic 0 and 8 has an automorphism of prime period without fixed points f^O, then 8 is nilpotent.1 In this note we give a proof valid also for characteristic p^O. By the same method we can prove several other similar results on automorphisms and derivations. Our method is based on decompositions of the Lie al...
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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 ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1988
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1988.132.209