Hacettepe University Bulletin of Natural Sciences and Engineering Series B Mathematics and Statistics, 2011
Abstract Let R be a prime ring and θ, φ endomorphisms of R. An additive mapping F: R−→ R is calle... more Abstract Let R be a prime ring and θ, φ endomorphisms of R. An additive mapping F: R−→ R is called a generalized (θ, φ)-derivation on R if there exists a (θ, φ)-derivation d: R−→ R such that F (xy)= F (x) θ (y)+ φ (x) d (y) for all x, y∈ R. Let S be a nonempty subset of R. In ...
International Journal of Mathematics and Mathematical Sciences, 2013
LetNbe a near ring. An additive mappingf:N→Nis said to be a right generalized (resp., left genera... more LetNbe a near ring. An additive mappingf:N→Nis said to be a right generalized (resp., left generalized) derivation with associated derivationdonNiff(xy)=f(x)y+xd(y)(resp.,f(xy)=d(x)y+xf(y)) for allx,y∈N. A mappingf:N→Nis said to be a generalized derivation with associated derivationdonNiffis both a right generalized and a left generalized derivation with associated derivationdonN. The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.
Hacettepe University Bulletin of Natural Sciences and Engineering Series B Mathematics and Statistics, 2011
Abstract Let R be a prime ring and θ, φ endomorphisms of R. An additive mapping F: R−→ R is calle... more Abstract Let R be a prime ring and θ, φ endomorphisms of R. An additive mapping F: R−→ R is called a generalized (θ, φ)-derivation on R if there exists a (θ, φ)-derivation d: R−→ R such that F (xy)= F (x) θ (y)+ φ (x) d (y) for all x, y∈ R. Let S be a nonempty subset of R. In ...
International Journal of Mathematics and Mathematical Sciences, 2013
LetNbe a near ring. An additive mappingf:N→Nis said to be a right generalized (resp., left genera... more LetNbe a near ring. An additive mappingf:N→Nis said to be a right generalized (resp., left generalized) derivation with associated derivationdonNiff(xy)=f(x)y+xd(y)(resp.,f(xy)=d(x)y+xf(y)) for allx,y∈N. A mappingf:N→Nis said to be a generalized derivation with associated derivationdonNiffis both a right generalized and a left generalized derivation with associated derivationdonN. The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.
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