CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS
Year 2021,
Volume: 29 Issue: 29, 50 - 62, 05.01.2021
M. A. Idrıssı
L. Oukhtıte
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.
References
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(1999), 4057-4073.
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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.
Year 2021,
Volume: 29 Issue: 29, 50 - 62, 05.01.2021
M. A. Idrıssı
L. Oukhtıte
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.