On Prime and Semiprime Rings with Symmetric Generalized Biderivations
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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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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Let F be a commuting generalized derivation, with associated derivation d, on a semiprime ring R. We show that d(x)[y, z] = 0 for all x, y, z ∈ R and d is central. We define and characterize dependent elements of F and investigate a decomposition of R relative to F . Mathematics Subject Classification: 16N60, 16W25
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An extensive generalized concept of classical ring set forth the notion of a gamma ring theory. As an emerging field of research, the research work of classical ring theory to the gamma ring theory has been drawn interest of many algebraists and prominent mathematicians over the world to determine many basic properties of gamma ring and to enrich the world of algebra. The different researchers ...
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.
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ژورنال
عنوان ژورنال: Al-Mustansiriyah Journal of Science
سال: 2017
ISSN: 2521-3520,1814-635X
DOI: 10.23851/mjs.v28i1.321