Generalized Derivations and Generalization of Co-commuting Maps in Prime Rings
نویسندگان
چکیده
منابع مشابه
Generalized 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 $R$ be a prime ring with its Utumi ring of quotients $U$, $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate} item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=...
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Let $R$ be a noncommutative prime ring of characteristic different from $2$, $U$ the Utumi quotient ring of $R$, $C$ $(=Z(U))$ the extended centroid of $R$. Let $0neq ain R$ and $f(x_1,ldots,x_n)$ a multilinear polynomial over $C$ which is noncentral valued on $R$. Suppose that $G$ and $H$ are two nonzero generalized derivations of $R$ such that $a(H(f(x))f(x)-f(x)G(f(x)))in ...
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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...
متن کاملPrime 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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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2021
ISSN: 1027-5487
DOI: 10.11650/tjm/200801