Multiplicative generalized derivations on ideals in semiprime rings
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Öznur Gölbaşi
Abstract
Let R be a ring and I is a nonzero ideal of R. A mapping F:R → R is called a multiplicative generalized derivation if there exists a mapping g:R → R such that F(xy) = F(x)y + xg(y), for all x, y ∈ R. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds:
F([x,y]) = 0,
F(xoy) = 0,
F([x,y]) = ± [x,y],
F(xoy) = ±(xoy),
F([x,y]) = ±(xoy),
F(xoy) = ±[x,y],
F([x,y]) = ±[F(x),y],
F(xoy) = ±(F(x)oy),
F(xy) ± xy ∈ Z,
F(xy) ± yx ∈ Z,
F(xy) ±[x,y] ∈ Z,
F(xy) ±(xoy) ∈ Z,
References
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© 2016 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- A triple representation of lattice effect algebras
- Periods of morgan-voyce sequences and elliptic curves
- Multiplicative generalized derivations on ideals in semiprime rings
- A few remarks on Poincaré-Perron solutions and regularly varying solutions
- Applications of extremal theorem and radius equation for a class of analytic functions
- On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
- New criteria for global exponential stability of linear time-varying volterra difference equations
- On approximation of functions by some hump matrix means of Fourier series
- Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
- Poisson kernels on semi-direct products of abelian groups
- Locally convex projective limit cones
- On the properties (wL) and (wV)
- On the existence of solutions for quadratic integral equations in Orlicz spaces
- Existence and uniqueness of best proximity points under rational contractivity conditions
- Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
- On the internal approach to differential equations 3. Infinitesimal symmetries
- A Characterization of the discontinuity point set of strongly separately continuous functions on products
- Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
- Multivariate EIV models
- On codes over 𝓡k, m and constructions for new binary self-dual codes
- Domination number of total graphs
