Main Article Content


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.


semiprime rings Ideal. Multiplicative (general) (a,1)-derivation

Article Details

How to Cite
Malleswari, G., Sreenivasulu, S., & Shobhalatha, G. (2022). Some Identities Involving Multiplicative (Generalized)(α; 1)-Derivations in Semiprime Rings. Journal of the Indonesian Mathematical Society, 28(1), 44–51.


  1. . Asma Ali, Ambreen Bano., Identities with Multiplicative (generalized)(α;b )-derivations in semiprime rings, Int. J. Math. and Appl., 6(4), (2018), 195-202.
  2. . Bresar, M., On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33, (1991), 89-93.
  3. . Bell, H. E., Martindale III, W. S., Centralizing mappings of semiprime rings, Canad. Math. Bull., 30(1), (1987), 92-101.
  4. . Chang, J. C, On the identity h (x) = af (x) + g (x) b, Taiwanese J. Math., 7(1), (2003), 103-113.
  5. . Daif, M. N., When is a Multiplicative derivation additive?, Int. J. Math. Sci., 14(3), (1991), 615-618.
  6. . Daif, M. N., Bell, H. E., Remarks on derivations on semiprime rings, Int. J. Math. Sci., 15(1), (1992), 205-206.
  7. . Daif, M. N and Tammam-El-Sayaid, M. S., Multiplicative generalized derivation which are additive, East-West J. Math., 9(1), (1997), 31-37.
  8. . Dhara, B and Ali. S., on Multiplicative (generalized)-derivations in prime and semiprime rings, A equat. Math., 86(1), (2013), 65-79.
  9. . Goldman, H and Semrl, P., Multiplicative derivations on C(x), Monatsh. Math., 121(3), (1996), 189-197.
  10. . Huang, S., Notes on commutativity of prime rings, Springer Proceedings in Mathematics and Statistics, ICAA., 174, (2016), 75-80.
  11. . Martindle III, W. S., When are multiplicative maps additive, proc. Am. Math. Soc., 21, (1969), 695-698.
  12. . Quadri, M. A, Khan. M. S, Rehman. N., Generalized derivations and commutativity of prime rings, Indian J. Pure Appl. Math., 34(9), (2003),1393-1396.
  13. . Samman, M. S, Thaheem, A. B, Derivations on semiprime rings, Int. J. Pure. Appl. Math., 5(4), (2003), 465-472.
  14. . Tammam-El-sayiad, M. S, Daif, M. N, and Filippis, V. D., Multiplicativity of left centralizers forcing additivity, Boc. Soc. Paran. Mat., 32(1), (2014), 61-69.