Semigroup ideal in Prime Near-Rings with Derivations
نویسندگان
چکیده
منابع مشابه
Generalized Derivations on Prime Near Rings
Let N be a near ring. An additive mapping f : N → N is said to be a right generalized (resp., left generalized) derivation with associated derivation d onN if f(xy) = f(x)y + xd(y) (resp., f(xy) = d(x)y + xf(y)) for all x, y ∈ N. A mapping f : N → N is said to be a generalized derivation with associated derivation d onN iff is both a right generalized and a left generalized derivation with asso...
متن کاملSemigroup ideals with semiderivations in 3-prime near-rings
The purpose of this paper is to obtain the structure of certain near-rings satisfying the following conditions: (i) d(I) ⊆ Z(N), (ii) d(−I) ⊆ Z(N), (iii) d([x, y]) = 0, (iv) d([x, y]) = [x, y], (v) d(x ◦ y) = 0, (vi) d(x ◦ y) = x ◦ y for all x, y ∈ I , with I is a semigroup ideal and d is a semiderivation associated with an automorphism. Furthermore; an example is given to illustrate that the 3...
متن کاملOn Prime-Gamma-Near-Rings with Generalized Derivations
Copyright q 2012 Kalyan Kumar Dey et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let N be a 2-torsion free prime Γ-near-ring with center ZN. Let f, d and g, h be two generalized derivations on N. We prove the following res...
متن کاملOn 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.
متن کاملGeneralized Derivations of Prime Rings
Let R be an associative prime ring, U a Lie ideal such that u2 ∈ U for all u ∈ U . An additive function F : R→ R is called a generalized derivation if there exists a derivation d : R→ R such that F(xy)= F(x)y + xd(y) holds for all x, y ∈ R. In this paper, we prove that d = 0 or U ⊆ Z(R) if any one of the following conditions holds: (1) d(x) ◦F(y)= 0, (2) [d(x),F(y) = 0], (3) either d(x) ◦ F(y) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Baghdad Science Journal
سال: 2011
ISSN: 2411-7986,2078-8665
DOI: 10.21123/bsj.8.3.810-814