Yazar "Albas, Emine" seçeneğine göre listele

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    Annihilators of Skew Derivations with Engel Conditions on Prime Rings
    (Springer Heidelberg, 2020) Pehlivan, Taylan; Albas, Emine
    LetRbe a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ringQ,Cthe extended centroid ofRanda is an element of R. Suppose that delta is a nonzero sigma-derivation ofRsuch thata[delta(x(n)),x(n)](k)= 0 for allx is an element of R, where sigma is an automorphism ofR,nandkare fixed positive integers. Thena= 0.
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    GENERALIZED DERIVATIONS ON IDEALS OF PRIME RINGS
    (Univ Miskolc Inst Math, 2013) Albas, Emine
    Let R be a prime ring. By a generalized derivation we mean an additive mapping g : R -> R such that g(xy) = g(x)y + xd(y) for all x, y is an element of R where d is a derivation of R. In the present paper our main goal is to generalize some results concerning derivations of prime rings to generalized derivations of prime rings.
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    GENERALIZED DERIVATIONS ON IDEALS OF PRIME RINGS
    (Univ Miskolc Inst Math, 2013) Albas, Emine
    Let R be a prime ring. By a generalized derivation we mean an additive mapping g : R -> R such that g(xy) = g(x)y + xd(y) for all x, y is an element of R where d is a derivation of R. In the present paper our main goal is to generalize some results concerning derivations of prime rings to generalized derivations of prime rings.
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    Posner's Second Theorem and some Related Annihilating Conditions on Lie Ideals
    (Univ Nis, Fac Sci Math, 2018) Albas, Emine; Argac, Nurcan; De Filippis, Vincenzo
    Let R be a non-commutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, L a non-central Lie ideal of R, Gamma and G two non-zero generalized derivations of R. If [F(u), u] G(u) = 0 for all u is an element of L, then one of the following holds: (a) there exists lambda is an element of C such that F(x) = lambda x, for all x is an element of R; (b) R subset of M-2(F), the ring of 2 X 2 matrices over a field F, and there exist a 2 U and lambda is an element of C such that F( x) = ax + xa + lambda x, for all x is an element of R.
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    Superderivations with invertible values
    (World Scientific Publ Co Pte Ltd, 2015) Demir, Cagri; Albas, Emine; Argac, Nurcan; Fosner, Ajda
    We examine the structure of unital associative superalgebras A having nonzero superderivations with zero or invertible values. Under some mild assumptions, we show that such a superalgebra A is either a division superalgebra D, or M-2(D), or it is a local superalgebra with a unique maximal graded ideal Msuch that M-2 = (0). We also describe in details the local superalgebras that are possible.
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    Superderivations with invertible values
    (World Scientific Publ Co Pte Ltd, 2015) Demir, Cagri; Albas, Emine; Argac, Nurcan; Fosner, Ajda
    We examine the structure of unital associative superalgebras A having nonzero superderivations with zero or invertible values. Under some mild assumptions, we show that such a superalgebra A is either a division superalgebra D, or M-2(D), or it is a local superalgebra with a unique maximal graded ideal Msuch that M-2 = (0). We also describe in details the local superalgebras that are possible.
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    Superderivations with invertible values
    (World Scientific Publ Co Pte Ltd, 2015) Demir, Cagri; Albas, Emine; Argac, Nurcan; Fosner, Ajda
    We examine the structure of unital associative superalgebras A having nonzero superderivations with zero or invertible values. Under some mild assumptions, we show that such a superalgebra A is either a division superalgebra D, or M-2(D), or it is a local superalgebra with a unique maximal graded ideal Msuch that M-2 = (0). We also describe in details the local superalgebras that are possible.
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    VANISHING DERIVATIONS AND CO-CENTRALIZING GENERALIZED DERIVATIONS ON MULTILINEAR POLYNOMIALS IN PRIME RINGS
    (Taylor & Francis Inc, 2016) Dhara, Basudeb; Argac, Nurcan; Albas, Emine
    Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x(1),...,x(n)) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) - f(r)G(f(r))) = 0 for all r = (r(1),...,r(n)) is an element of R-n, then one of the following holds: 1) There exist a, p, q, c is an element of U and lambda is an element of C such that F(x) = ax + xp + lambda x, G(x) = px + xq and d(x) = [c, x] for all x is an element of R, with [c, a - q] = 0 and f (x(1),...,x(n))(2) is central valued on R; (2) There exists a is an element of U such that F(x) = xa and G(x) = ax for all x is an element of R; (3) There exist a, b, c is an element of U and lambda is an element of C such that F(x) = lambda x + xa - bx, G(x) = ax + xb and d(x) = [c, x] for all x is an element of R, with b + alpha c is an element of C for some alpha is an element of C; (4) R satisfies s(4) and there exist a, b is an element of U and lambda is an element of C such that F(x) = lambda x + xa - bx and G(x) = ax + xb for all x is an element of R; (5) There exist a', b, c is an element of U and delta a derivation of R such that F(x) = a' x + xb - delta(x), G(x) = bx + delta(x) and d(x) = [c, x] for all x is an element of R, with [c , a'] = 0 and f(x(1),...,x(n))(2) is central valued on R.