Left annihilator of identities with generalized derivations in prime and semiprime rings
نویسندگان
چکیده
منابع مشابه
Left Annihilator of Identities Involving Generalized Derivations in Prime Rings
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 with its Utumi ring of quotients U , C = Z(U) the extended centroid of R, F a generalized derivation of R and I a nonzero ideal of R. Suppose that there exists 0 = a ∈ R such that a(F ([x, y]) − [x, y]) = 0 for all x, y ∈ I, where n ≥ 2 is a fixed integer. Then one of the following holds: 1. char (R) = 2, R ⊆ M2(C), F (x) = bx for all x ∈ R with a(b − 1) = 0...
متن کاملRemarks on Generalized Derivations in Prime and Semiprime Rings
Let R be a ring with center Z and I a nonzero ideal of R. An additive mapping F : R → R is called a generalized derivation of R if there exists a derivation d : R → R such that F xy F x y xd y for all x, y ∈ R. In the present paper, we prove that if F x, y ± x, y for all x, y ∈ I or F x ◦ y ± x ◦ y for all x, y ∈ I, then the semiprime ring R must contains a nonzero central ideal, provided d I /...
متن کاملLie Ideals and Generalized Derivations in Semiprime Rings
Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.
متن کاملIdentities with derivations and automorphisms on semiprime rings
The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae - General Algebra and Applications
سال: 2021
ISSN: 1509-9415,2084-0373
DOI: 10.7151/dmgaa.1356