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[PDF] Top 20 On Prime Gamma Near Rings with Generalized Derivations

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On Prime Gamma Near Rings with Generalized Derivations

On Prime Gamma Near Rings with Generalized Derivations

... In this section we prove that a few subsidiary results Lemmas 3.1, 3.2, 3.4, 3.8, 3.9, 3.10 and 3.11 to use them for proving of our main results Theorems 3.3, 3.5, 3.6, 3.12 and 3.13. Lemma 3.1. Let d be an arbitrary ... See full document

15

Optimized Multiplicative Derivations in Close to Rings

Optimized Multiplicative Derivations in Close to Rings

... 3-prime near-rings admitting different types of derivations, generalized derivations, generalized multiplicative derivations( for reference see [1, 3, 4, 5, 6, 7, ... See full document

7

Vanishing Power Values of Commutators with Derivations on Prime Rings

Vanishing Power Values of Commutators with Derivations on Prime Rings

... for all x, y ∈ R. Since d / 0, a / ∈ C and hence R satisfies a nontrivial generalized polynomial identity GPI. By 11, it follows that RC is a primitive ring with H SocRC / 0, and eHe is finite dimensional over C ... See full document

8

On Prime Near Rings with Generalized Derivation

On Prime Near Rings with Generalized Derivation

... Suppose now that N is 2-torsion-free and that DZ / {0}, and let z ∈ Z be such that Dz / 0. Then if x, y ∈ N and fNx {0}, then fyzx fyzx yDzx 0 yDzx; and since N is 3-prime and Dz is not a zero divisor, x 0. It now ... See full document

5

(1,α)- Derivations in Prime г - near Rings

(1,α)- Derivations in Prime г - near Rings

... of near rings, rings were introduced by ...a near ring has been introduced by Bell and ...of derivations in near ...in prime and semiprime rings admitting suitably ... See full document

7

On Semigroup Ideals and Left Generalized (ɵ,ɵ)-4- Derivations in Prime Near-Rings

On Semigroup Ideals and Left Generalized (ɵ,ɵ)-4- Derivations in Prime Near-Rings

... a near –ring and is a mapping on N ...left generalized ( , )-4-derivation in near-ring N and we determine some conditions of left generalized ( , )-4-derivation and semigroup ideals which make ... See full document

5

Remarks on Generalized Derivations in Prime and Semiprime Rings

Remarks on Generalized Derivations in Prime and Semiprime Rings

... Proof. Let d be the associated derivation of F. By Theorem 2.4, we conclude that either dI 0 or R is commutative. Assume that R is not commutative. Then dI 0. Since R is a prime ring, dI 0 implies dR 0 and hence ... See full document

6

Identities in $3$-prime near-rings with left multipliers

Identities in $3$-prime near-rings with left multipliers

... left generalized derivation with associated derivation d if F(xy) = d(x)y + xF (y), for all x, y ∈ N ...a generalized derivation with associated derivation d if it is both a left as well as a right ... See full document

11

Left Generalized Derivations on Prime Γ-Rings

Left Generalized Derivations on Prime Γ-Rings

... a prime -ring with 2-torsion free and a nonzero ideal of ...a generalized derivation and left generalized derivation of , with associated derivation d on ... See full document

5

Left Annihilator of Identities Involving Generalized Derivations in Prime Rings

Left Annihilator of Identities Involving Generalized Derivations in Prime Rings

... associative prime ring with center Z (R) and U the Utumi quotient ring of ...of generalized derivation: An additive mapping F : R → R is called generalized derivation, if there exists a derivation d ... See full document

13

Right (θ,θ)-4-Derivations on Prime Near-Rings

Right (θ,θ)-4-Derivations on Prime Near-Rings

... a near –ring and is a mapping on N ...in near-ring N and we determine some conditions of right ( , )-4-derivation which make prime near-ring commutative ring ... See full document

6

ClosedLieIdeals of Prime Rings with Generalizedα−derivations

ClosedLieIdeals of Prime Rings with Generalizedα−derivations

... be prime with𝑐ℎ𝑎𝑟 𝑅 ≠ 2, (0) ≠ 𝐿 be a square closed Lie ideal of 𝑅 and 0 ≠ 𝐹, 𝐺: 𝑅 → 𝑅 are generalized 𝛼 − derivations associated with 𝛼 − derivations 𝑑 and 𝑔 respectively such that 𝑠 ∈ 𝑍(𝐿)|0 ... See full document

9

A Note on Generalized Skew Derivations on Rings

A Note on Generalized Skew Derivations on Rings

... a generalized skew-derivation of R if there exists a skew-derivation D of R with associated automorphism α such that G(xy)=G(x)y+α(x)D(y) for all ...of generalized skew-derivation is a unified notion of ... See full document

10

Derivations Acting as Homomorphisms and as Anti homomorphisms in σ Lie Ideals of σ Prime Gamma Rings

Derivations Acting as Homomorphisms and as Anti homomorphisms in σ Lie Ideals of σ Prime Gamma Rings

... a generalized derivation of a prime Γ-ring M with an associated derivation d of M which acts as a homomorphism and an anti-homomorphism on a non-zero ideal I of M , then d = 0 or M is ... See full document

6

On Prime and Semiprime Rings with Additive Mappings and Derivations

On Prime and Semiprime Rings with Additive Mappings and Derivations

... a generalized derivation of R. The notion of generalized derivation was introduced by Breˇ sar ...of generalized derivations of prime ...a generalized derivation of R. Thus, ... See full document

8

Skew   Commuting Derivations of Noncommutative Prime Rings

Skew Commuting Derivations of Noncommutative Prime Rings

... on rings help us to understand rings better and also derivations on rings can tell us about the structure of the ...Also derivations can be helpful for relating a ring with the set of ... See full document

5

Lie Ideals on Prime Γ-Rings with Jordan Right Derivations

Lie Ideals on Prime Γ-Rings with Jordan Right Derivations

... a prime Γ -ring ܯ for which ܯ is commutative with the conditions ݀(ܷ) ⊆ ܷ and ݀ ଶ (ܷ) ⊆ ܼ , where ܷ is an ideal of ܯ and ܼ is the centre of ܯ ...completely prime Γ -ring which is a ...completely ... See full document

10

Left Generalized Derivations and Commutativity of Prime Rings

Left Generalized Derivations and Commutativity of Prime Rings

... a prime ring and be a nonzero ideal of . If admits a left generalized derivation associated with a nonzero derivation such that ( ) + = 0holds for all , ∈ , then is ... See full document

5

On Commutativity of *-Prime Near-Rings with Derivations

On Commutativity of *-Prime Near-Rings with Derivations

... studied derivations in ∗-prime rings and proved the following: Let R be a ∗-prime ring having nonzero ∗-ideal I then (i) If d is a nonzero derivation on R which commutes with ∗ and [x, R]Id(x) ... See full document

12

Generalized Derivations on Prime Near Rings

Generalized Derivations on Prime Near Rings

... left near ring with multiplicative center 𝑍, and for any pair of elements 𝑥, 𝑦 ∈ 𝑁, [𝑥, 𝑦] denotes the commutator 𝑥𝑦 − 𝑦𝑥, while the symbol (𝑥, 𝑦) denotes the additive commutator ...A near ring 𝑁 is called ... See full document

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