GENERALIZED JORDAN TRIPLE $(\theta,\phi)$-DERIVATIONS ON SEMIPRIME RINGS

Liu, Cheng-Kai; Shiue, Wen-Kwei

doi:10.11650/twjm/1500404872

Cited by 36 publications

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“…The concept of generalized derivation has been introduced by Bresar [4]. Hvala [11] and Lee [18] introduced a concept of (θ, φ)-derivation (see also [19]). An additive mapping…”

Section: Since Then the Stability Problems Of Various Functional Equamentioning

confidence: 99%

Stability of homomorphisms and (θ,ф)-derivations

Najati

Rassias

2009

APPL ANAL DISCRETE M

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“…The concept of generalized derivation has been introduced by Bresar [4]. Hvala [11] and Lee [18] introduced a concept of (θ, φ)-derivation (see also [19]). An additive mapping…”

Section: Since Then the Stability Problems Of Various Functional Equamentioning

confidence: 99%

Stability of homomorphisms and (θ,ф)-derivations

Najati

Rassias

2009

APPL ANAL DISCRETE M

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“…An additive mapping ξ : R → R is called a generalized (θ, ϕ)-derivation if there exists a (θ, ϕ)-derivation δ : R → R such that ξ(xy) = ξ(x)θ(y) + ϕ(x)δ(y) holds for all x, y ∈ R (see [6], [11]). In [13], Liu and Shiue proved that every Jordan (triple) (θ, ϕ)-derivation on a 2-torsion free semiprime ring is a (θ, ϕ)-derivation. Also, they introduced a concept of generalized Jordan (θ, ϕ)-derivation and generalized Jordan triple (θ, ϕ)-derivation (see also [10]).…”

Section: Introductionmentioning

confidence: 99%

“…A result of [1] states that every generalized Jordan (θ, ϕ)-derivation is a generalized Jordan triple (θ, ϕ)-derivation. Liu and Shiue [13] proved that every generalized Jordan (triple) (θ, ϕ)-derivation on a 2-torsion free semiprime ring is a generalized (θ, ϕ)-derivation (see also [14]). …”

Section: Introductionmentioning

confidence: 99%

On generalized Jordan derivations of Lie triple systems

Najati

2010

Czech Math J

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“…Thus [xp, y] = 0 for all x, y ∈ R. Then we have [x, y] zp = 0 for all x, y, z ∈ R. It follows that R is commutative or p = 0. If p = 0, then λ(x) = 0 for all x ∈ R by (12). If [x, y] = 0, then from (12) follows that λ(x)y − λ(y)x = 0 for all x, y ∈ R. Consequently λ = 0.…”

mentioning

confidence: 99%

“…If p = 0, then λ(x) = 0 for all x ∈ R by (12). If [x, y] = 0, then from (12) follows that λ(x)y − λ(y)x = 0 for all x, y ∈ R. Consequently λ = 0. Now suppose that R is a PI ring.…”

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confidence: 99%

On certain functional equation arising from (m,n)- Jordan centralizers in prime rings

Peršin¹,

Vukman²

2012

Glas. Mat. Ser. III

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Abstract. The purpose of this paper is to prove the following result. Let m ≥ 1, n ≥ 1 be some fixed integers and let R be a prime ring with char(R) = 0 or (m + n) 2 < char(R). Suppose there exists an additive mapping T : R → R satisfying the relation 2(m + n) 2 T (x 3 ) = m(2m + n)T (x)x 2 + 2mnxT (x)x + n(2n + m)x 2 T (x) for all x ∈ R. In this case T is a two-sided centralizer.Throughout, R will represent an associative ring with center Z(R). Given an integer n ≥ 2, a ring R is said to be n−torsion free, if for x ∈ R, nx = 0 implies x = 0. As usual the commutator xy − yx will be denoted by [x, y]. We shall use the commutator identities [xy, z] Recall that a ring R is prime if for a, b ∈ R, aRb = (0) implies that either a = 0 or b = 0 and is semiprime in case aRa = (0) implies a = 0. We denote by char(R) the characteristic of a prime ring R. An additive mapping D : R → R, where R is an arbitrary ring, is called a derivation if D(xy) = D(x)y + xD(y) holds for all pairs x, y ∈ R, and is called a Jordan derivation in case D(x 2 ) = D(x)x + xD(x) is fulfilled for all x ∈ R. A derivation D is inner in case there exists a ∈ R, such that D(x) = [a, x] holds for all x ∈ R. Every derivation is a Jordan derivation. The converse is in general not true. A classical result of Herstein ([10]) asserts that any Jordan derivation on a prime ring with char(R) = 2 is a derivation. A brief proof of Herstein's result can be found in [3]. Cusack 2010 Mathematics Subject Classification. 16W10, 46K15, 39B05.

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GENERALIZED JORDAN TRIPLE $(\theta,\phi)$-DERIVATIONS ON SEMIPRIME RINGS

Cited by 36 publications

References 0 publications

Stability of homomorphisms and (θ,ф)-derivations

Stability of homomorphisms and (θ,ф)-derivations

On generalized Jordan derivations of Lie triple systems

On certain functional equation arising from (m,n)- Jordan centralizers in prime rings

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