On Lie Structure of Prime Rings with Generalized (\alpha\beta, )-Derivations
نویسندگان
چکیده
منابع مشابه
Prime Lie Rings of Generalized Derivations of Commutative Rings
Let R be a commutative ring with identity. By a Bres̃ar generalized derivation of R we mean an additive map g : R→ R such that g (xy) = g (x) y + xd (y) for all x, y ∈ R, where d is a derivation of R. And an additive mapping f : R → R is called a generalized derivation in the sense of Nakajima if it satisfies f(xy) = f(x)y + xf(y) − xf(1)y for all x, y ∈ R. In this paper we extend some results o...
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Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that usH(u)ut = 0 for all u ∈ L, where s ≥ 0, t ≥ 0 are fixed integers. Then H(x) = 0 for all x ∈ R unless char R = 2 and R satisfies S4, the standard identity in four variables. Let R be an associative ring with center Z(R). For x, y ∈ R, the commutator xy− yx will be denoted by [x, y]. An add...
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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 اولGeneralized Derivations of Prime Rings
Let R be an associative prime ring, U a Lie ideal such that u2 ∈ U for all u ∈ U . An additive function F : R→ R is called a generalized derivation if there exists a derivation d : R→ R such that F(xy)= F(x)y + xd(y) holds for all x, y ∈ R. In this paper, we prove that d = 0 or U ⊆ Z(R) if any one of the following conditions holds: (1) d(x) ◦F(y)= 0, (2) [d(x),F(y) = 0], (3) either d(x) ◦ F(y) ...
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Let N be a near ring. An additive mapping f : N → N is said to be a right generalized (resp., left generalized) derivation with associated derivation d onN if f(xy) = f(x)y + xd(y) (resp., f(xy) = d(x)y + xf(y)) for all x, y ∈ N. A mapping f : N → N is said to be a generalized derivation with associated derivation d onN iff is both a right generalized and a left generalized derivation with asso...
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ژورنال
عنوان ژورنال: Boletim da Sociedade Paranaense de Matemática
سال: 2010
ISSN: 2175-1188,0037-8712
DOI: 10.5269/bsmp.v27i2.10209