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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.
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.