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G. Malleswari
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Mathematics

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Some Identities Involving Multiplicative (Generalized)(α; 1)-Derivations in Semiprime Rings G. Malleswari; S. Sreenivasulu; G. Shobhalatha
Journal of the Indonesian Mathematical Society VOLUME 28 NUMBER 1 (MARCH 2022)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.28.1.992.44-51

Abstract

Let R be a semiprime ring, I a non-zero ideal of R and α be an automorphism of R. A map F : R to R is said to be a multiplicative (generalized)(α, 1)-derivation associated with a map d : R to R such that F (xy) = F (x) α (y) + xd (y), for all x, y in R. In the present paper, we shall prove that R contains a non-zero central ideal if any one of the following holds: (i) F [x, y] ± [x,y] =0; (ii) F (xoy)±α(xoy) = 0; (iii) F [x, y] = [F (x) , y]α;1 ; (iv) F [x, y] =(F (x) oy)α;1 ; (v) F (xoy) = [F(x) , y]α;1 and (vi)F (xoy) = (F (x) oy)α;1, for all x, y in I.
Co-Authors G. Shobhalatha S. Sreenivasulu