[PDF] Top 20 A note on (α,β)*-i-n-Derivations in Rings with Involution
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A note on (α,β)*-i-n-Derivations in Rings with Involution
... with involution ‘∗’. In this paper we introduce the notion of (α, β)-∗-i-n-derivation in ...an involution on R if it satisfies the conditions; (i) (x ∗ ) ∗ = x, (ii) (xy) ∗ = y ∗ x ∗ ... See full document
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A Characterization of Derivations in Prime Rings with Involution
... de- note by Q and C the maximal ring of quotient and the extended centroid of a prime ring, ...an involution if ∗ is an anti-automorphism of order 2; that is, (x ∗ ) ∗ = x for all x ∈ ...with ... See full document
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$\Gamma$*-Derivation Pair and Jordan $\Gamma$*-Derivation Pair on $\Gamma$-ring M with Involution
... theory. Note that during the last few decades, many authors have studied derivations in the context of prime and semiprime rings and Γ-rings with involution ... See full document
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Characterization of Jordan *-derivations by local action on rings with involution
... . Note that, if R is 2-torsion free, then a Jordan *-derivation can be equivalently defined as δ(ab + ba) = δ(a)b ∗ + aδ(b) + δ(b)a ∗ + bδ(a) for all a, b ∈ R 0 ... See full document
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A Note on Generalized Skew Derivations on Rings
... an involution if * is an anti-automorphism of order 2; that is (x*)*=x for all ...with involution * is said to be hermitian and skew-hermitian elements of R will be denoted by H(R) and S(R), ...The ... See full document
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On Commutativity of *-Prime Near-Rings with Derivations
... ∈ I in the relation ...∈ I, by Lemma 2.4. If d(I) = {0}, then for any s ∈ N we get d(sx) = d(s)x = 0 for all x ∈ I ...d(s)N I = {0} = d(s)N I ∗ and as ... See full document
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Symmetric Skew Reverse n-Derivations on Prime Rings and Semiprime rings
... Let n be any integer. A ring R is said to be n- torsion free, if for all x, y R, n x = 0 x = ...Let I be any non-empty two sided ideal of ...on I, if [ (x) , x ] = 0 , x ... See full document
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Generalized Multiplicative Derivations in Near-Rings
... ∈ N . (3.1) Replacing y by yr where r ∈ N in ...∈ N . Hence by 3-primeness of N , for each x ∈ N either d(x) = 0 or x ∈ ...∈ N . For otherwise, we have d(uv) = 0 for all v ∈ ... See full document
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Identities in $3$-prime near-rings with left multipliers
... ∈ N and F is called a left generalized derivation with associated derivation d if F(xy) = d(x)y + xF (y), for all x, y ∈ N ...: N → N is said to be a left ...semiprime rings admitting ... See full document
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On commutativity of prime and semiprime rings with generalized derivations
... ring, I a nonzero ideal of R and m, n are fixed positive ...d(y)) n = 0 for all x, y ∈ I, then either R is commutative or there exist b ∈ U , Utumi ring of quotient of R such that F (x) = bx ... See full document
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Optimized Multiplicative Derivations in Close to Rings
... ∈ N . (3.2) Case I: Let f = ...∈ N . Replacing x by xr, where r ∈ N in the previous relation and using the same relation again we arrive at N [r, y] = {0} ...of N , we conclude ... See full document
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On some equations related to derivations in rings
... Jordan derivations on rings, ...left derivations, ...[11] I. N. Herstein, Jordan derivations of prime rings, ...Posner, Derivations in prime rings, ...prime ... See full document
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Identities with derivations and automorphisms on semiprime rings
... with derivations and automorphisms on semiprime ...− I , where I denotes the identity mapping, map R into its ...by I the identity mapping of a ring ...R. Note that the mapping D = α − ... See full document
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Rings with involution whose symmetric elements are central
... The classification of such rings which are 2-torsion free is equivalent to the classification of Lie algebras.. that is symmetric, invariant and satisfies If.[r] ... See full document
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On the Lie ring of derivations of a semiprime ring
... Throughout the text R stands for an associative ring (possibly without identity) and n for a positive integer. By Z(R) we denote the center of R. The ring R is called semiprime, if it has no nonzero nilpotent ... See full document
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(1,α)- Derivations in Prime г - near Rings
... near rings, rings were introduced by ...of derivations in near ...semiprime rings admitting suitably constrained derivations and generalized derivations, and several authors have ... See full document
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On locally nilpotent derivations of Fermat rings
... Let R be a ring. An additive mapping D : R → R is said to be a derivation of R if it satisfies the Leibniz rule: D(ab) = aD(b) + D(a)b, for all a, b ∈ R. If A ≤ R is a subring and D is a derivation of R satisfying D(A) = ... See full document
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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 of U ... See full document
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Generalized Derivations on Prime Near Rings
... Now consider the case 𝑑 ̸= 0. Let 𝑐 ∈ 𝑍 \ {0}. This implies that if 𝑥 ∈ 𝑈 , 𝑓(𝑥𝑐) = 𝑓(𝑥)𝑐 + 𝑥𝑑(𝑐) ∈ 𝑍 . Thus (𝑓(𝑥)𝑐 + 𝑥𝑑(𝑐))𝑦 = 𝑦(𝑓(𝑥)𝑐 + 𝑥𝑑(𝑐)) for all 𝑥, 𝑦 ∈ 𝑈 and 𝑐 ∈ 𝑍 . Therefore by Lemma 5(i), 𝑓(𝑥)𝑐𝑦+𝑥𝑑(𝑐)𝑦 ... See full document
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Dependent Elements of Derivations on Semiprime Rings
... semiprime rings; in particular a von Neumann algebra is prime if and only if its centre consists of the scalar multiples of identity ...semiprime rings and prime ... See full document
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