On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings

  • Chirag Garg Department of Mathematics, Deshbandhu College, University of Delhi, India
  • R. K. Sharma Department of Mathematics, Indian Institute of Technology Delhi, India
Keywords: multiplicative (generalized)-derivations

Abstract

UDC 512.5

We discuss some algebraic identities related to multiplicative (generalized)-derivations and multiplicative (generalized)-$(\alpha,\beta)$-derivations on appropriate subsets in prime rings.

References

E. Albas, Generalized derivations on ideals of prime rings, Miskolc Math. Notes, 14, 3–9 (2002).

S. Ali, B. Dhara, N. A. Dar, A. N. Khan, On Lie ideals with multiplicative (generalized)-derivations in prime and semiprime rings, Beitr. Algebra und Geom. (2014); DOI:10.1007/s13366-013-186-y.

M. Ashraf, N. Rehman, On commutativity of rings with derivations, Results Math., 42, 3–8 (2002).

H. E. Bell, M. N. Daif, On derivations and commutativity in prime rings, Acta Math. Hungar., 66, 337–343 (1995).

J. Bergen, I. N. Herstein, J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71, 259–267 (1981).

M. Brešar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33, 89–93 (1991).

M. N. Daif, H. E. Bell, Remarks on derivations on semiprime rings, Int. J. Math. and Math. Sci., 15, 205–206 (1992).

M. N. Daif, M. S. Tammam El-Sayiad, Multiplicative generalized derivations which are additive, East-West J. Math., 9, 31–37 (1997).

M. N. Daif, When is a multiplicative derivation additive, Int. J. Math. and Math. Sci., 14, 615–618 (1991).

B. Dhara, S. Ali, On multiplicative (generalized)-derivations in prime and semiprime rings, Aequationes Math., 86, 65–79 (2013).

B. Dhara, S. Kar, D. Das, A multiplicative (generalized)-$(σ,σ)$-derivation acting as (anti-)homomorphism in semiprime rings, Palest. J. Math., 3, 240–246 (2014).

C. Garg, R. K. Sharma, On generalized $(α,β)$-derivations in prime rings, Rend. Circ. Mat. Palermo, 65, 175–184 (2016).

O. Golbasi, E. Koc, Generalized derivations of Lie ideals in prime rings, Turk. J. Math., 35, 23–28 (2011).

H. Goldmann, P. Šemrl, Multiplicative derivations on $C(X)$, Monatsh. Math., 121, 189–197 (1996).

S. Khan, On semiprime rings with multiplicative (generalized)-derivations, Beitr. Algebra und Geom. (2015); DOI: 10.1007/s13366-015-0241-y.

E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8, 1093–1100 (1957).

N. Rehman, On commutativity of rings with generalized derivations, Math. J. Okayama Univ., 44, 43–49 (2002).

Published
28.02.2024
How to Cite
Garg, C., and R. K. Sharma. “On Multiplicative (generalized)-$(\alpha,\beta)$-Derivations in Prime Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, no. 2, Feb. 2024, pp. 289-97, doi:10.3842/umzh.v76i2.654.
Section
Research articles