On semiderivations of *-prime rings
DOI:
https://doi.org/10.5269/bspm.v33i2.23687Abstract
Let R be a ∗-prime ring with involution ∗ and center Z(R). An additive mapping F:R→R is called a semiderivation if there exists a function g:R→R such that (i) F(xy)=F(x)g(y)+xF(y)=F(x)y+g(x)F(y) and (ii) F(g(x))=g(F(x)) hold for all x,y∈R. In the present paper, some well known results concerning derivations of prime rings are extended to semiderivations of ∗-prime rings.
References
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2. Bergen, J., Derivations in prime rings, Canad. Math. Bull., 26, (1983), 267-270.
3. Chang, J. C., On semiderivations of prime rings, Chinese J. Math., 12, (1984), 255-262.
4. Daif, M. N., Bell, H. E., Remarks on derivations on semiprime rings, Internat J. Math. and Math. Sci., 15(1), (1992), 205-206.
5. Herstein, I. N., A note on derivations II, Canad. Math. Bull., 22(4), (1979), 509-511.
6. Oukhtite, L., Salhi, S., On commutativity of ∗−prime rings, Glasnik Mathematicki, 41, (2006), 57-64.
7. Oukhtite, L., Salhi, S., On generalized derivations of ∗−prime rings, African Diaspora J. Math., 5(1), (2006), 19-23.
8. Oukhtite, L., Salhi, S., Lie ideals and derivations of ∗−prime rings, Int. J. Algebra, 1, (2007), 25-30.
9. Oukhtite, L., Salhi, S., Centralizing automorphisms and Jordan left derivations on ∗−prime rings, Adv. Algebra 1(1), (2008), 19-26.
10. Oukhtite, L., Salhi, S., Taoufiq, L., Commutativity conditions on derivations and Lie ideals in ∗−prime rings, Beitrage Algebra Geom., 51(1), (2010), 275-282.
11. Posner, E. C., Derivations in prime rings, Proc Amer. Math. Soc., 8, (1957), 1093-1100.
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2014-08-19
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