Nonexistence of nonzero derivations on some classes of zero-symmetric 3-prime near-rings
نویسندگان
چکیده
منابع مشابه
On 3-prime Near-rings with Generalized Derivations
We prove some theorems in the setting of a 3-prime near-ring admitting a suitably constrained generalized derivation, thereby extending some known results on derivations. Moreover, we give an example proving that the hypothesis of 3-primeness is necessary.
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Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x), x], [d(y), y]] = 0, for all x, y ∈ I. We prove that if [I, I]I ≠ 0, then d(I)I = 0. 1. Introduction. Let R be a prime ring and d a nonzero derivation of R. Define [x, y] 1 = [x, y] = xy − yx, then an Engel condition is a polynomial [x, y] k = [[x, y] k−1 ,y]
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ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 2014
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-014-0945-4