MULTIPLIERS AND REVERSE GENERALIZED (α, ∗)-n-DERIVATIONS ON PRIME RINGS
MULTIPLIERS AND REVERSE GENERALIZED (α, ∗)-n-DERIVATIONS
DOI:
https://doi.org/10.5269/bspm.78792Abstract
While α is an automorphism of R and ∗ denotes involution of R,
the goal of the current study is to define the notion of reverse generalized (α, ∗)-
derivations on ring R. Using the roles of α and ∗, we derive certain commutativity
theorems in the case of prime rings. The proofs of the theorems in the situation of a
non-commutative prime ring and the conditions under which a reverse generalized
(α, ∗)-derivation acts as a α-multiplier will also be covered. Appropriate examples
are provided to support the proposed idea.
References
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derivations, Aequationes Mathematicae, (2012), 1-9.
[2] Ansari, A. Z. and Shujat, F., Jordan ∗-derivations on Standard Operator Algebras, Filomat,
37(1) (2023), 37–41.
[3] Ansari, A. Z. and Shujat, F., Kamel, A., Fallatah, A., Jordan φ-centralizers on Semiprime
and Involution Rings, European Journal of Pure and Applied Mathematics, 18 (1) (2025),
5493-5493.
[4] Bell H. E. and Martindale III W. S., Centralizing mappings of semiprime rings, Canad. Math.
Bull., 30, 92–101 (1987).
[5] Breˇsar M., On the distance of the composition of two derivations to the generalized derivations,
Glasgow Math. J., 33, No. 1, 89–93 (1991).
[6] Bresar, M. and Vukman, J., On some additive mappings in rings with involution, Aequationes
Math., 38(1989), 178-185.
[7] Divinsky, N., On commuting automorphisms of rings, Trans. Roy. Soc. Canada Sect. III, 49
(1955), 19-22.
[8] Herstein I. N., Jordan derivations of prime rings, Proc. Amer. Math. Soc., 8, No. 6, 1104–1110
(1957).
[9] Johnson, B. E., An introduction to the theory of centralizers, Proc. London Math. Soc., 14
(1964), 299-320.
[10] Larsen, R., An Introduction to the Theory of Multipliers, Springer-Verlag, Berlin, 1971.
[11] Luh, J., A note on commuting automorphisms of rings, Amer. Math. Monthly, 77 (1970),
61-62.
[12] Mayne, J. H., Centralizing automorphisms of prime rings, Canad. Math. Bull., 19 (1976),
113-115.
[13] Samman M. S. and Alyamani N., Derivations and reverse derivations in semiprime rings, Int.
Math. Forum, 2, No. 39, 1895–1902 (2007).
[14] Wang, J. K., Multipliers of commutative Banach algebras, Pacific. J. Math., 11 (1961), 1131-
1149.
[15] Zalar, B., On multipliers of semiprime rings, Comment. Math. Univ. Carol., 32 (1991), 609-
614.
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2026-03-29
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