Multiplicative (generalized)-derivations of prime rings that act as $n$-(anti)homomorphisms
Keywords:
prime rings; multiplicative (generalized)-derivations; n-homomorphisms; n-antihomomorphisms
Abstract
Let R be a prime ring. In this note, we describe the possible forms of multiplicative (generalized)-derivations of R that act as n-homomorphism or n-antihomomorphism on nonzero ideals of R. Consequently, from the given results one can easily deduce the results of Gusić ([7]).
References
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2. H.E. Bell, L.C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hung., 53 (1989), No3–4, 339–346. doi: 10.1007/BF01953371
3. M. Brešar, Semiderivations of prime rings, Proc. Amer. Math. Soc., 108 (1990), No4 , 859–860. doi: 10.1090/S0002-9939-1990-1007488-X
4. M. Brešar, On the distance of the composition of two derivations to the generalized derivations, Glasg. Math. J., 33 (1991), 89–93. doi:
10.1017/S0017089500008077
5. J.-C. Chang, Right generalized (α, β)−derivations having power central values, Taiwanese J. Math., 13 (2009), No4, 1111–1120. doi: 10.11650/twjm/1500405495
6. B. Dhara, S. Ali, On multiplicative (generalized)-derivations in prime and semiprime rings, Aequ. Math., 86 (2013), No1–2, 65–79. doi: 10.1007/s00010-013-0205-y
7. I. Gusić, A note on generalized derivations of prime rings, Glasnik Mate., 40 (2005), No1, 47–49.
8. S. Hejazian, M. Mirzavaziri, M. Moslehian, n-homomorphisms, Bull. Iran. Math. Soc., 31 (2005), No1, 13–23.
9. C. Lanksi, An Engel condition with derivation, Proc. Amer. Math. Soc., 118 (1993), No3, 731–734. doi: 10.1090/S0002-9939-1993-1132851-9
10. M.P. Lukashenko, Derivations as homomorphisms and anti−homomorphisms in differentialy semiprime rings, Mat. Stud., 43 (2015), No1, 12–15. doi: 10.15330/ms.43.1.12-15
11. N. Rehman, On generalized derivations as homomorphisms and anti-homomorphisms, Glasnik Mate., 39 (2004), No1, 27–30.
2. H.E. Bell, L.C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hung., 53 (1989), No3–4, 339–346. doi: 10.1007/BF01953371
3. M. Brešar, Semiderivations of prime rings, Proc. Amer. Math. Soc., 108 (1990), No4 , 859–860. doi: 10.1090/S0002-9939-1990-1007488-X
4. M. Brešar, On the distance of the composition of two derivations to the generalized derivations, Glasg. Math. J., 33 (1991), 89–93. doi:
10.1017/S0017089500008077
5. J.-C. Chang, Right generalized (α, β)−derivations having power central values, Taiwanese J. Math., 13 (2009), No4, 1111–1120. doi: 10.11650/twjm/1500405495
6. B. Dhara, S. Ali, On multiplicative (generalized)-derivations in prime and semiprime rings, Aequ. Math., 86 (2013), No1–2, 65–79. doi: 10.1007/s00010-013-0205-y
7. I. Gusić, A note on generalized derivations of prime rings, Glasnik Mate., 40 (2005), No1, 47–49.
8. S. Hejazian, M. Mirzavaziri, M. Moslehian, n-homomorphisms, Bull. Iran. Math. Soc., 31 (2005), No1, 13–23.
9. C. Lanksi, An Engel condition with derivation, Proc. Amer. Math. Soc., 118 (1993), No3, 731–734. doi: 10.1090/S0002-9939-1993-1132851-9
10. M.P. Lukashenko, Derivations as homomorphisms and anti−homomorphisms in differentialy semiprime rings, Mat. Stud., 43 (2015), No1, 12–15. doi: 10.15330/ms.43.1.12-15
11. N. Rehman, On generalized derivations as homomorphisms and anti-homomorphisms, Glasnik Mate., 39 (2004), No1, 27–30.
Published
2020-06-27
How to Cite
Sandhu, G. (2020). Multiplicative (generalized)-derivations of prime rings that act as $n$-(anti)homomorphisms. Matematychni Studii, 53(2), 125-133. https://doi.org/10.30970/ms.53.2.125-133
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Copyright (c) 2020 G.S. Sandhu
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