Yazar "Yarbil, Nihan Baydar" seçeneğine göre listele

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    Annihilators and centralizers of generalized skew derivations on multilinear polynomials
    (Springer Heidelberg, 2018) Yarbil, Nihan Baydar; De Filippis, Vincenzo; Scudo, Giovanni
    Let R be a prime ring of characteristic different from 2, Q(r) its right Martindale quotient ring, C its extended centroid, a, b. R, f (x1,..., xn) a non-central multilinear polynomial over C with n non-commuting variables and G a non-zero generalized skew derivation of R. Assume a = 0, b /. C, S = {f (r1,..., rn) : r1,..., rn. R} and a[b, G(x) x] = 0, for all x. S. Then one of the following holds: (a) there exists c. Q(r) such that ac = abc = 0 and G(x) = cx, for any x. R; (b) f (x1,..., xn) 2 is central valued on R and there exists c. Q(r) su ch that a[b, c] = 0 and G(x) = cx, for any x is an element of R.
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    Annihilators of Power Central Values of Generalized Skew Derivations on Lie Ideals
    (Tarbiat Modares Univ, Acecr, 2024) Yarbil, Nihan Baydar; Argac, Nurcan
    Let R be a prime ring with center Z(R) and G be a generalized alpha -derivation of R for alpha is an element of Aut (R). Let a E R be a nonzero element and n be a fixed positive integer. (i) If aG (x)(n) is an element of Z ( R ) for all x is an element of R then aG (x) = 0 for all x is an element of R unless dim(C) RC = 4. (ii) If aG (x)(n) E Z ( R ) for all x is an element of L , where L is a noncommutative Lie ideal of R then aG (x) = 0 for all x is an element of R unless dim(C) RC = 4.
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    ANNIHILATORS OF POWER VALUES OF b-GENERALIZED DERIVATIONS IN PRIME RINGS
    (2020) Yarbil, Nihan Baydar
    Let R be a prime ring with extended centroid C and maximal left ring of quotients Qml(R). For a nonzero element b 2 R, let T : R ? R be a right b-generalized derivation associated with the map d of R. Suppose that s (T (x))n = O for all x 2 R where s is a nonzero element in R and n ? 1 is a fixed positive integer. Then there exist some c 2 Qml(R) and ? 2 C such that d(x) = adc(x), T (x) = (c + ?)xb for all x 2 R and either s(c + ?) = O or b(c + ?) = O.
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    ANNIHILATORS OF POWER VALUES OF b-GENERALIZED DERIVATIONS IN PRIME RINGS
    (Ankara Univ, Fac Sci, 2020) Yarbil, Nihan Baydar
    Let R be a prime ring with extended centroid C and maximal left ring of quotients Q(ml)(R). For a nonzero element b is an element of R, let F : R -> R be a right b-generalized derivation associated with the map d of R. Suppose that s (F(x))(n) = 0 for all x is an element of R where s is a nonzero element in R and n >= 1 is a.xed positive integer. Then there exist some c is an element of Q(ml)(R) and beta is an element of C such that d(x) = ad(c)(x), F(x) = (c + beta)xb for all x is an element of R and either s(c + beta) = 0 or b(c + beta) = 0.
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    A note on generalized Lie derivations of prime rings
    (Higher Education Press, 2017) Yarbil, Nihan Baydar; Argac, Nurcan
    Let R be a prime ring of characteristic not 2, A be an additive subgroup of R, and F, T, D, K: A-R be additive maps such that F([x, y]) = F(x) (y-y) K(x)-T(y) (x + x) D(y) for all x, y E A. Our aim is to deal with this functional identity when A is R itself or a noncentral Lie ideal of R. Eventually, we are able to describe the forms of the mappings F, T, D, and K in case A = R with deg(R) > 3 and also in the case A is a noncentral Lie ideal and deg(R) > 9. These enable us in return to characterize the forms of both generalized Lie derivations, D-Lie derivations and Lie centralizers of R under some mild assumptions. Finally, we give a generalization of Lie homomorphisms on Lie ideals.
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    A quadratic differential identity with skew derivations
    (Taylor & Francis Inc, 2018) Yarbil, Nihan Baydar; De Filippis, Vincenzo
    Let R be, a prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C, and let f(xi xn) be a multilinear polynomial over C, not central valued on R. Suppose that F and G are skew derivations of R, associated with the automorphism, such that F(f(r(1), ...,r(n)))G(f(r(1),...,r(n))) + G(f(r(1), ..., r(n)))F(f(r(1), ..., r(n))) = 0. for all r1, ..., rn R. Then either F 0 or G -= 0