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[PDF] Top 20 On derivations and commutativity in prime rings

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On derivations and commutativity in prime rings

On derivations and commutativity in prime rings

... Fact 2 . Any derivation of R can be uniquely extended to a derivation of Q, and so any derivation of R can be defined on the whole of Q [1, Proposition 2.5.1]. Moreover, Q is a prime ring as well as R and the ... See full document

7

On Commutativity of *-Prime Near-Rings with Derivations

On Commutativity of *-Prime Near-Rings with Derivations

... Abstract: The primary purpose of this paper is to introduce the notion of ∗-prime near-rings, which is a special class of distributive near-rings and to investigate their commutativity. Let N ... See full document

12

Symmetric Skew Reverse n-Derivations on Prime
Rings and Semiprime rings

Symmetric Skew Reverse n-Derivations on Prime Rings and Semiprime rings

... reverse derivations of prime rings was introduced by Bresar and Vukman ...between derivations and reverse derivations with examples were given by Samman and Alyamani ...on ... See full document

6

Left Generalized Derivations and Commutativity of Prime Rings

Left Generalized Derivations and Commutativity of Prime Rings

... the commutativity of prime rings with derivations was initiated by ...generalized derivations in prime ...on prime ring is ...of prime rings. ... See full document

5

On commutativity of near rings with generalized derivations

On commutativity of near rings with generalized derivations

... of commutativity of 3-prime near-rings by using derivations was initiated by Bell and Mason in 1987 in ...from rings to near-rings with derivations in ...generalized ... See full document

11

Results of Symmetric Reverse bi-derivations on Prime Rings

Results of Symmetric Reverse bi-derivations on Prime Rings

... The concept of a symmetric bi-derivation has been introduced by Maksa in [6]. In [9], Vukman has proved some results concerning symmetric bi-derivation on prime and semiprime rings. Yenigul and Argac [10] ... See full document

6

Strong commutativity preserving biderivations on prime rings

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 ... See full document

7

Generalized Derivations of Prime Rings

Generalized Derivations of Prime Rings

... the derivations and Lie ideals of a prime ring, and obtain some useful ...of commutativity on a prime ...a prime ring. Throughout this paper, R will be a prime ring and U will ... See full document

6

On Jordan ideals and left (θ,θ) derivations in prime rings

On Jordan ideals and left (θ,θ) derivations in prime rings

... where 1 is the identity mapping on R. In [5], Brešar and Vukman have proved that the existence of a nonzero Jordan left derivation on a prime ring R of charR ≠ 2,3 forces R to be commutative. It should be ... See full document

8

ClosedLieIdeals of Prime Rings with Generalizedα−derivations

ClosedLieIdeals of Prime Rings with Generalizedα−derivations

... on prime ringswithgeneralized𝛼 − derivation. Let 𝑅 be a prime ring and 𝑐ℎ𝑎𝑟𝑅 ≠ 2, 𝐿 be a square closed Lie ideal of 𝑅 and 0 ≠ 𝐹: 𝑅 → 𝑅 be a generalized 𝛼 − derivation associated with 𝛼 − derivation 𝑑 such ... See full document

9

Left Annihilator of Identities Involving Generalized Derivations in Prime Rings

Left Annihilator of Identities Involving Generalized Derivations in Prime Rings

... Let R be an associative prime ring with center Z (R) and U the Utumi quotient ring of R. The center of U, denoted by C, is called the extended centroid of R (we refer the reader to [2] for these objects). For ... See full document

13

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

Generalized derivations in prime rings

Generalized derivations in prime rings

... a prime ring R which acts as homomorphisms or anti-homomorphisms on a nonzero right ideal of R then d = 0 on ...free prime ring and I be a non zero ideal of ...a prime ring with a non-zero ideal I of ... See full document

5

Vanishing Power Values of Commutators with Derivations on Prime Rings

Vanishing Power Values of Commutators with Derivations on Prime Rings

... a prime ring R can be uniquely extended to a derivation of Q, and so any derivation of R can be defined on the whole of ...a prime ring as well as R and the extended centroid C of R coincides with the ... See full document

8

On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings

Afrah Mohammad Ibraheem

On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings Afrah Mohammad Ibraheem

... called prime if aΓRΓb = 0 with a, b ∈R implies a = 0 or b = 0, and R is called semi prime if aΓRΓa = 0 with a ∈R implies a = ...semi-) prime Γ-ring is an extension for the notion of a ... See full document

6

Generalized Multiplicative Derivations in Near-Rings

Generalized Multiplicative Derivations in Near-Rings

... of commutativity of 3-prime near-rings was initiated by using derivations by ...the commutativity of 3-prime near-rings admitting different types of derivations, ... See full document

9

Left Generalized Derivations on Prime Γ-Rings

Left Generalized Derivations on Prime Γ-Rings

... Generalized derivations in ...Generalized derivations in semiprime gamma rings Bresar [2] studied on the distance of the composition of two derivations to the generalized ...on prime ... See full document

5

On Prime and Semiprime Rings with Additive Mappings and Derivations

On Prime and Semiprime Rings with Additive Mappings and Derivations

... mapping d : R −→ R is called a derivation if d(xy) = d(x)y + xd(y) holds for all x, y ∈ R. Let F, d : R −→ R be two mappings such that F(xy) = F (x)y + xd(y) holds for all x, y ∈ R. If F is additive and d is a derivation ... See full document

8

On Prime Gamma Near Rings with Generalized Derivations

On Prime Gamma Near Rings with Generalized Derivations

... The derivations in Γ-near-rings have been introduced by Bell and Mason ...of derivations in Γ-near-rings. Then As¸ci 2 obtained commutativity conditions for a Γ-near-ring with ...the ... See full document

15

Optimized Multiplicative Derivations in Close to Rings

Optimized Multiplicative Derivations in Close to Rings

... of derivations, generalized derivations, generalized multiplicative derivations( for reference see [1, 3, 4, 5, 6, 7, 8, 9], where further references can be ...the commutativity of ... See full document

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