Semiprime rings
Dependent Elements of Derivations on Semiprime Rings
... of semiprime rings and on the other hand by the work done by various researchers on commuting derivations on prime and semiprime rings, we investigate some properties, not already ...
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Lie Ideals and Generalized Derivations in Semiprime Rings
... Abstract. 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 → R such that F(xy) = F (x)y+xd(y) holds for all ...
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A note on a pair of derivations of semiprime rings
... a semiprime ring with center Z(R), and let f , g be derivations of R such that f (x)x + xg(x) ∈ Z(R) for all x ∈ R, then f and g are ...a semiprime ring R is ...
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On Prime and Semiprime Rings with Additive Mappings and Derivations
... Abstract Let R be an associative ring. A mapping f : R −→ R is said to be additive if f (x + y) = f (x) + f (y) holds for all x, y ∈ R. An additive mapping d : R −→ R is called a derivation if d(xy) = d(x)y + xd(y) holds ...
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Identities 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 ...
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On Finite Rank Operators on Centrally Closed Semiprime Rings
... nonzero ideal I of R (resp. if IJ ≠ 0 for all nonzero ideals , I J of R ). The center C of Q R s ( ) is called the extended centroid of R , and the C -subring Q R : = RC of Q R s ( ) generated by R is called the central ...
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On commutativity of prime and semiprime rings with generalized derivations
... Fact 2.2. [Lee, 1999, Theorem 4] Let R be a semiprime ring. Then every gen- eralized derivation F on a dense right ideal of R is uniquely extended to U and assumes the form F (x) = ax + d(x) for some a ∈ U and a ...
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On Symmetric Reverse Ɵ*-Bicentralizer in Semiprime *- Rings
... Theorem 3.8 : Let R be a 2-torsion free semiprime *- ring , then every symmetric right Jordan * - Bicentralizer of R is a symmetric right reverse * - Bicentralizer . Where is an automorphism on R Lemma 3.9 : Let R ...
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Annihilator condition of a pair of derivations in prime and semiprime rings
... P ROOF : Since any derivation d can be uniquely extended to a derivation in U , and U and R satisfy the same differential identities ( see [20]), then ad(x) ∈ Z(U ), for all x ∈ U . Let P ∈ M(C) such that U/P U is ...
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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 Fxy Fxy xdy for all x, y ∈ R. In the ...
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Symmetric Skew Reverse n-Derivations on Prime Rings and Semiprime rings
... “Semiprime ring with Symmetric skew 3-reverse derivations”, Trans. on Math., 1 (2015), 11-15. [11] C. Jayasubba Reddy, V.Vijaya Kumar and S.Mallikarjuna Rao, “Prime ring with symmetric skew 4-reverse derivation”, ...
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Generalized Derivations in Semiprime Gamma Rings
... Hvala 1 first introduced the generalized derivations in rings and obtained some remarkable results in classical rings. Daif and Tammam El-Sayiad 2 studied the generalized derivations in semiprime ...
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Strong commutativity preserving biderivations on prime rings
... It was shown in [6] that symmetric biderivations are related to general solution of some functional equations. The notion of additive commuting mappings is closely connected with the notion of biderivations. Every ...
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On dependent elements in rings
... on F . It is easy to see that in semiprime rings there are no nonzero nilpotent dependent elements (see [11]). This fact will be used throughout the paper without specific refer- ences. Dependent elements ...
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Left Annihilator of Identities Involving Generalized Derivations in Prime Rings
... for all x, y ∈ U . Let M (C) be the set of all maximal ideals of C and P ∈ M (C). Now by the standard theory of orthogonal completions for semiprime rings (see [24, p.31-32]), we have P U is a prime ideal ...
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(1,α)- Derivations in Prime г - near Rings
... near rings, rings were introduced by ...and semiprime rings admitting suitably constrained derivations and generalized derivations, and several authors have proved comparable results on ...
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A note on (α,β)*-i-n-Derivations in Rings with Involution
... Recently Ashraf et.al. [6, Theorem 3.1] proved that if a prime ∗-ring R admits a nonzero ∗-n-derivation D, then R is commutative. We have proved its analogue for (α, β)-∗-i-n- derivation in the setting of ∗-prime ...
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Jordan automorphisms, Jordan derivations of generalized triangular matrix algebra
... A well-know result of Herstein [11] states that every Jordan isomorphism on a prime ring of characteristic di ff erent from 2 is either an isomorphism or an anti-isomorphism. We remark that the situation where the ...
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$\Gamma$*-Derivation Pair and Jordan $\Gamma$*-Derivation Pair on $\Gamma$-ring M with Involution
... Barnes [3], Luh [13], Kyuno [11], Hoque and Paul [8] as well as Uddin and Islam [16,17] studied the structure of Г-rings and obtained various generalizations of corresponding parts in ring theory. Note that ...
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Vol 9, No 3 (2018)
... and semiprime rings. The study of derivations of near-rings was initiated by ...and semiprime rings admitting suitably constrained derivations and generalized derivations ...
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