CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS

Year 2021, , 50 - 62, 05.01.2021

M. A. Idrıssı L. Oukhtıte

https://doi.org/10.24330/ieja.852003

Abstract

The purpose of the present paper is to classify generalized derivations satisfying more specific algebraic identities in a prime ring with
involution of the second kind. Some well-known results
characterizing commutativity of prime rings by derivations have
been generalized by using generalized derivation.

Keywords

Prime ring, involution, commutativity, derivation, generalized derivation

References

• S. Ali and N. A. Dar, On *-centralizing mapping in rings with involution, Georgian Math. J., 21(1) (2014), 25-28.
• S. Ali, N. A. Dar and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J., 23(1) (2016), 9-14.
• M. Ashraf, N. Rehman, S. Ali and M. R. Mozumder, On semiprime rings with generalized derivations, Bol. Soc. Parana. Mat., (3), 28(2) (2010), 25-32.
• M. Bresar, Semiderivations of prime rings, Proc. Amer. Math. Soc., 108(4) (1990), 859-860.
• M. Bresar, On generalized biderivations and related maps, J. Algebra, 172(3) (1995), 764-786.
• V. De Filippis, N. Rehman and A. Ansari, Lie ideals and generalized deriva- tions in semiprime rings, Iran. J. Math. Sci. Inform., 10(2) (2015), 45-54.
• B. Hvala, Generalized derivations in rings, Comm. Algebra, 26 (1998), 1147- 1166.
• M. A. Idrissi and L. Oukhtite, Some commutativity theorems for rings with involution involving generalized derivations, Asian-Eur. J. Math., 12(1) (2019), 1950001 (11 pp).
• C. Lanski, Differential identities, Lie ideals and Posner's theorems, Pacific J. Math., 134(2) (1988), 275-297.
• M. R. Khan and M. M. Hasnain, On semiprime rings with generalized derivations, Kyungpook Math. J., 53(4) (2013), 565-571.
• T. K. Lee, Generalized derivations of left faithful rings, Comm. Algebra, 27 (1999), 4057-4073.
• B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, Certain commutativity criteria for rings with involution involving generalized derivations, Georgian Math. J., 27(1) (2020), 133-139.
• L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math., 38(2) (2014), 225-232.
• E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.