On Prime and Semiprime Rings with Additive Mappings and Derivations
نویسندگان
چکیده
منابع مشابه
Remarks 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 /...
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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 $(1-e)U$. ...
متن کاملCentralizers on prime and semiprime rings
The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let R be a noncommutative prime ring of characteristic different from two and let S and T be left centralizers on R. Suppose that [S(x), T (x)]S(x) + S(x)[S(x), T (x)] = 0 is fulfilled for all x ∈ R. If S 6= 0 (T 6= 0) then there exists λ from the extende...
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We prove in this note the following result. Let n > 1 be an integer and let R be an n!torsion-free semiprime ring with identity element. Suppose that there exists an additive mapping D : R→ R such that D(xn) =∑nj=1 xn− jD(x)x j−1is fulfilled for all x ∈ R. In this case, D is a derivation. This research is motivated by the work of Bridges and Bergen (1984). Throughout, R will represent an associ...
متن کاملOn Identities with Additive Mappings in Rings
begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}
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ژورنال
عنوان ژورنال: Universal Journal of Computational Mathematics
سال: 2014
ISSN: 2332-3035,2332-3043
DOI: 10.13189/ujcmj.2014.020302