[PDF] Top 20 Generalized Multiplicative Derivations in Near-Rings

... left near-ring. N is called a 3-prime near-ring if xN y = {0} implies x = 0 or y = ...semiprime near-ring if xN x = {0} implies x = ...the multiplicative center of N , that is, Z = {x ∈ N | xy ... See full document

... 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

... with multiplicative centre ZN. Recall that a Γ-near-ring N is prime if xΓNΓy 0 implies x 0 or y ...a generalized derivation if there exits a derivation d of N such that fxαy f xαy xαdy for all x, y ∈ ... See full document

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

... 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

... right near-ring with multiplicative center Z(N ...right near-ring N is called zero-symmetric if x0 = 0 for all x ∈ N (recalling that right distributivity yields 0x = ...in rings has been ... See full document

... left near- ring. N is called a prime near-ring if xN y = {0} implies x = 0 or y = ...1, near-ring N is said to be n-torsion free, if for x ∈ N , nx = 0 implies x = ...the multiplicative center ... See full document

... left near-ring, not necessarily with a multiplicative identity element; and let Z be its multiplicative ...A generalized derivation f with associated derivation D is an additive endomorphism f ... See full document

... Proof. We prove only (ii), since (i) is proved in [2]. For all 𝑥, 𝑦, 𝑧 ∈ 𝑁 we have 𝑓((𝑥𝑦)𝑧) = 𝑓(𝑥𝑦)𝑧 + 𝑥𝑦𝑑(𝑧) = (𝑑(𝑥)𝑦+𝑥𝑓(𝑦))𝑧+𝑥𝑦𝑑(𝑧) and 𝑓(𝑥(𝑦𝑧)) = 𝑑(𝑥)𝑦𝑧+𝑥𝑓(𝑦𝑧) = 𝑑(𝑥)𝑦𝑧 + 𝑥𝑓(𝑓(𝑦)𝑧 + 𝑦𝑑(𝑧)) = 𝑑(𝑥)𝑦𝑧 + 𝑥𝑓(𝑦)𝑧 + 𝑥𝑦𝑑(𝑧). ... See full document

... d(Z(R)) = {0}, a contradiction. So the assumption d(Z(R)) = {0} is not true. 2 Theorem 3.3 — Let R be a 3-prime near-ring with a non-zero generalized derivation f such that f (U ) ⊆ Z(R), where U is a ... See full document

... a generalized derivation, if there exists a derivation d : R → R such that F(xy) = F(x)y + xd(y) holds for all x, y ∈ ...of generalized derivations covers both the concepts of a derivation and a left ... See full document

... A well-known result proven by Posner 1 states that if dx, x, y 0 for all x, y ∈ R, then R is commutative. In 2, Lanski generalized this result of Posner to the Lie ideal. Lanski proved that if U is a ... See full document

... Theorem 3.2. Let be a prime -ring with 2-torsion free and a nonzero ideal of . Let : → be a generalized derivation and left generalized derivation of , with associated derivation d on . If ∈ and [(), ] ... See full document

... Lemma 1.2. Let R be a prime ring of characteristic different from 2 and L be a Lie ideal of R. Suppose R admits a nonzero generalized derivation (F, d) such that F(x)[x, y] = 0 (or [x, y]F (x) = 0) for all x, y ∈ ... See full document

... a generalized derivation if there exists a derivation d:R→R such that D(xy) = D(x)y + xd(y) for all ...Two generalized derivations (D, d) and (G, g) of R are called orthogonal if D(x)RG(y) = 0 = ... See full document

... of τ-torsion submodules of M. A torsion theory will be called hereditary if T is closed under submodules and it will be called cohereditary if F is closed under factor modules. Standard results and terminology on torsion ... See full document

... Suppose by contradiction that R does not satisfy any nontrivial generalized polynomial identity.. We divide the proof into two cases.[r] ... See full document

... Moreover, Manikantan [10] introduced the notion of fuzzy bi-ideals of near-rings and discussed the some of its properties. Cho et al. [5] introduced the concept of weak bi-ideals and applied it to ... See full document

... Γ -ring is one of the most important and modern branches of algebra in mathematics now a days. In this paper we tried to characterize some special properties of prime Γ -ring on Lie ideals with Jordan right ... See full document

... a near –ring and is a mapping on N ...in near-ring N and we determine some conditions of ( , )-3-derivation and semigroup ideals which make prime near-ring commutative ring ... See full document