Yazar "Aydin, Neset" seçeneğine göre listele

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    Öğe
    A note on (?,?)-derivations in prime rings
    (Springer India, 2008) Aydin, Neset
    Let R be a 2-torsion free prime ring and let sigma, tau be automorphisms of R. For any x, y epsilon R, set [x, y](sigma,tau) = x sigma(y) - tau(y)x. Suppose that d is a (sigma, tau)-derivation defined on R. In the present paper it is shown that (i) if d is a nonzero (sigma, tau)-derivation andh is a nonzero derivation of R such that dh(R) (subset of) over dot C sigma,tau then R is commutative. (ii) if R satisfies [d(x), x](sigma,tau) epsilon C-sigma,C-tau, then either d = 0 or R is commutative. (iii) if I is a nonzero ideal of R such that d(xy) = d(yx) for all x, y epsilon I, then R is commutative.
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    Generalized *-Lieideal of *-primering
    (Tubitak Scientific & Technological Research Council Turkey, 2017) Turkmen, Selin; Aydin, Neset
    Let R be a *-prime ring with characteristic not 2, sigma,tau : R -> R be two automorphisms, U be a nonzero *-(sigma, tau)-Lie ideal of R such that tau commutes with *, and a,b be in R. (i) If a is an element of S*(R) and [U, a] - 0, then a is an element of Z (R) or U subset of Z (R) : (ii) If a is an element of S* ( R) and [U,a](sigma),(tau) subset of C-sigma,C-tau, then a is an element of Z (R) or U subset of Z (R). (iii) If U not subset of Z (R) and U not subset of C-sigma,C-tau, then there exists a nonzero *-ideal M of R such that [R, M](sigma, tau) subset of U but [R, M](sigma,tau) not subset of C-sigma,C-tau . (iv) Let U not subset of Z (R) and U not subset of C-sigma,C-tau . If aUb = a*U b = 0, then a = 0 or b = 0 :
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    Öğe
    On *-(?, T)-Lie ideals of *-prime rings with derivation
    (Hacettepe Univ, Fac Sci, 2018) Aydin, Neset; Koc, Emine; Golbasi, Oznur
    Let R be a (*)-prime ring with characteristic not 2, U be a nonzero (*)- (sigma, tau)-Lie ideal of R and d be a nonzero derivation of R. Suppose sigma, tau be two automorphisms of R such that sigma d = d sigma, tau d = d tau and * commutes with sigma, tau, d. In the present paper it is shown that if d(2)(U) = (0), then U subset of Z.
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    Öğe
    ON A LIE RING OF GENERALIZED INNER DERIVATIONS
    (Korean Mathematical Soc, 2017) Aydin, Neset; Turkmen, Selin
    In this paper, we define a set including of all f(a) with a is an element of R generalized derivations of R and is denoted by f(R). It is proved that (i) the mapping g : L (R) -> f(R) given by g (a) = f(-a) for all a is an element of R is a Lie epimorphism with kernel N-sigma,N-tau; (ii) if R is a semiprime ring and sigma is an epimorphism of R, the mapping h : f(R) -> I (R) given by h(f(a)) = i(sigma)(-a) is a Lie epimorphism with kernel 1 (f(R)); (iii) if f(R) is a prime Lie ring and A, B are Lie ideals of R, then [f(A), f(B)] = (0) implies that either f(A) = (0) or f(B) = (0).
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    ON DERIVATIONS SATISFYING CERTAIN IDENTITIES ON RINGS AND ALGEBRAS
    (Univ Nis, 2019) Sandhu, Gurninder S.; Kumar, Deepak; Camci, Didem K.; Aydin, Neset
    The present paper deals with the commutativity of an associative ring R and a unital Banach Algebra A via derivations. Precisely, the study of multiplicative (generalized)-derivations F and G of semiprime (prime) ring R satisfying the identities G(xy) +/- [F(x), y] +/- [x, y] is an element of Z(R) and G(xy) +/- [x , F(y)] +/- [x, y] is an element of Z(R) has been carried out. Moreover, we prove that a unital prime Banach algebra A admitting continuous linear generalized derivations F and G is commutative if for any integer n > 1 either G((xy)(n)) + [F(x(n)), y(n) ] + [x(n),y(n)] is an element of Z(A) or G((xy(n)) - [F(x(n)), y(n)] - [x(n) , y(n)] is an element of Z(A).
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    ON MULTIPLICATIVE (GENERALIZED)-DERIVATIONS IN SEMIPRIME RINGS
    (Ankara Univ, Fac Sci, 2017) Camci, Didem K.; Aydin, Neset
    In this paper, we study commutativity of a prime or semiprime ring using a map F : R -> R, multiplicative (generalized) -derivation and a map H : R -> R, multiplicative left centralizer, under the following conditions: For all x,y is an element of R, i) F(xy) +/- H(xy) = 0, ii) F(xy) +/- H(yx) = 0, iii) F(x)F(y) +/- H(xy) = 0, iv) F(xy) +/- H(xy) is an element of Z, v) F(xy) +/- H(yx) is an element of Z, vi) F(x)F(y) +/- H(xy) is an element of Z.
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    ON NEAR-RING IDEALS WITH (?,t)-DERIVATION
    (Masaryk Univ, Fac Science, 2007) Golbasi, Oznur; Aydin, Neset
    Let N be a 3-prime left near-ring with multiplicative center Z, a (sigma, tau)-derivation D on N is defined to be an additive endomorphism satisfying the product rule D (x y) = tau (x) D (y)+ D (x) sigma (y) for all x, y 2 N, where sigma and tau are automorphisms of N. A nonempty subset U of N will be called a semigroup right ideal (resp. semigroup left ideal) if U N subset of U (resp. N U subset of U) and if U is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let D be a (sigma, tau)-derivation on N such that sigma D = D sigma, tau D = D tau. (i) If U is semigroup right ideal of N and D (U) subset of Z then N is commutative ring. (ii) If U is a semigroup ideal of N and D (2) (U) = 0 then D = 0. (i i i) If a is an element of N and [D (U), a] sigma, tau = 0 then D (a) = 0 or a is an element of Z.
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    Öğe
    Regular elements of the complete semigroups of binary relations of the class ?6(X, 8)
    (Walter De Gruyter Gmbh, 2015) Aydin, Neset; Diasamidze, Yasha; Sungur, Didem Yesil
    In this paper, let X be a finite set, D be a complete X-semilattice of unions and Q = {T-1, T-2, T-3, T-4, T-5, T-6, T-7, T-8} be an X-subsemilattice of D where T-1 subset of T-3 subset of T-5 subset of T-6 subset of T-8, T-1 subset of T-3 subset of T-5 subset of T-7 subset of T-8, T-2 subset of T-3 subset of T-5 subset of T-6 subset of T-8, T-2 subset of T-3 subset of T-5 subset of T-7 subset of T-8, T-2 subset of T-4 subset of T-5 subset of T-6 subset of T-8, T-2 subset of T-4 subset of T-5 subset of T-7 subset of T-8, T-2 \ T-1 not equal empty set, T-1 \ T-2 not equal empty set, T4 \ T-3 not equal empty set, T-3 \ T-4 not equal empty set, T-6 \ T-7 not equal empty set, T-7 \ T-6 not equal empty set, T-2 boolean OR T-1 = T-3, T-4 boolean OR T-3 = T-5, T-6 boolean OR T-7 = T-8. Using the characteristic family of sets, the characteristic mapping and base sources of Q, we characterize the class whose elements are each isomorphic to Q. We generate some advanced formulas in order to calculate the number of regular elements alpha of B-X (D) satisfying V (D, alpha) = Q, in an efficient way.
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    Some results on ?-ideal of ?-prime ring
    (Hacettepe Univ, Fac Sci, 2015) Turkmen, Selin; Aydin, Neset
    Let R be a sigma-prime ring with characteristic not 2, Z (R) be the center of R, I be a nonzero sigma-ideal of R, alpha, beta : R -> R be two automorphisms, d be a nonzero (alpha, beta)-derivation of R and h be a nonzero derivation of R : In the present paper, it is shown that (i) If d (I) subset of C-alpha,C-beta and beta commutes with sigma then R is commutative. (ii) Let alpha and beta commute with sigma. If a is an element of I boolean AND S-sigma (R) and [d(I), a](alpha,beta) subset of C-alpha,C-beta then a is an element of Z(R). (iii) Let alpha, beta and h commute with sigma. If dh (I) subset of C-alpha,C- beta and h(I) subset of I then R is commutative.
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    Öğe
    THE SOURCE OF SEMIPRIMENESS OF RINGS
    (Korean Mathematical Soc, 2018) Aydin, Neset; Demir, Cagri; Camci, Didem Karalarlioglu
    Let R be an associative ring. We define a subset S-R of R as S-R = {a is an element of R vertical bar aRa = (0)} and call it the source of semiprimeness of R. We first examine some basic properties of the subset S-R in any ring R, and then define the notions such as R being a vertical bar S-R vertical bar-reduced ring, a vertical bar S-R vertical bar-domain and a vertical bar S-R vertical bar-division ring which are slight generalizations of their classical versions. Beside others, we for instance prove that a finite vertical bar S-R vertical bar-domain is necessarily unitary, and is in fact a vertical bar S-R vertical bar-division ring. However, we provide an example showing that a finite vertical bar S-R vertical bar-division ring does not need to be commutative. All possible values for characteristics of unitary vertical bar S-R vertical bar-reduced rings and vertical bar S-R vertical bar-domains are also determined.