Semiprime near-rings with multiplicative generalized (θ,θ)-derivations
2016
artykuł naukowy
angielski
- semiprime near-ring
- semigroup ideal
- generalized derivation
- multiplicative generalized derivation
- multiplicative generalized (θ‚θ)-derivation
EN Let N be a semiprime right near-ring and I a semigroup ideal of N. A map f : N → N is called a multiplicative generalized (θ, θ)-derivation if there exists a multiplicative (θ, θ)-derivation d : R → R such that f(xy) = f(x)θ(y) + θ(x)d(y), for all x,y ϵ R. The purpose of this paper is to investigate the following: (i) f(uv) = ±uv, (ii) f(uv) = ±vu, (iii) f(u)f(v) = ±uv, (iv) f(u)f(v) = ±vu, (v) d(u)d(v) = θ([u,v]), (vi) d(u)d(v) = θ(uov), (vii) d(u)θ(v) = θ(u)d(v).
105 - 119
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