Jordan triple (α,β)-higher ∗-derivations on semiprime rings

• Autorzy: Ezzat Osama Hamed

Identyfikatory

DOI

10.1515/dema-2022-0213

• Języki publikacji: EN

Abstrakty

EN

In this article, we define the following: Let N0 be the set of all nonnegative integers and D=(di)i∈N0 a family of additive mappings of a ∗ -ring R such that d0=idR . D is called a Jordan (α,β) -higher ∗ -derivation (resp. a Jordan triple (α,β) -higher ∗ -derivation) of R if dn(a2)=∑i+j=n di(βj(a))dj(αi(a∗i)) (resp. dn(aba)=∑i+j+k=n di(βj+k(a))dj(βk(αi(b∗i)))dk(αi+j(a∗i+j)) ) for all a,b∈R and each n∈N0 . We show that the two notions of Jordan (α,β) -higher ∗ -derivation and Jordan triple (α,β) -higher ∗ -derivation on a 6-torsion free semiprime ∗ -ring are equivalent.

Słowa kluczowe

EN

semiprime rings; involutions; derivations; Jordan ∗-derivations; higher derivations

PL

pierścienie; pierścienie pierwsze; potęgowania; pochodne; pochodne Jordana

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220213
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Ezzat Osama Hamed

• Department of Mathematics, College of Science and Arts at Balgarn, University of Bisha, Sabt Al-Alaya(61985), Saudi Arabia
• Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt

• https://orcid.org/0000-0002-8605-3693

Bibliografia

• [1] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), no. 6, 1104–1110, DOI: https://doi.org/10.2307/2032688.
• [2] A. Fošner and W. Jing, A note on Jordan derivations of triangular rings, Aeq. Math. 94 (2020), no. 2, 277–285, DOI: https://doi.org/10.1007/s00010-019-00689-y.
• [3] N. Rehman, O. Golbasi, and E. Koc, Lie ideals and ( )α β, -derivations of ∗-prime rings, Rend. Circ. Mat. Palermo 62 (2013), no. 2, 245–251, DOI: https://doi.org/10.1007/s12215-013-0119-5.
• [4] N. A. Dar and S. Ali, On the structure of generalized Jordan ∗-derivations of prime rings, Comm. Algebra 49 (2020), no. 4, 1422–1430, DOI: https://doi.org/10.1080/00927872.2020.1837148.
• [5] O. H. Ezzat, Functional equations related to higher derivations in semiprime rings, Open Math. 19 (2021), no. 1, 1359–1365, DOI: https://doi.org/10.1515/math-2021-0123.
• [6] I. N. Herstein, Topics in Ring Theory, University of Chicago Press, Chicago, 1969.
• [7] M. Brešar, Jordan mappings of semiprime rings, J. Algebra. 127 (1989), no. 1, 218–228. DOI: https://doi.org/10.1016/0021-8693(89)90285-8.
• [8] M. Brešar and J. Vukman, On some additive mappings in rings with involution, Aequationes Math. J. 38 (1989), no. 2, 178–185. DOI: https://doi.org/10.1007/BF01840003.
• [9] P. Šemrl, Quadratic functionals and Jordan ∗-derivations, Studia Math. 97 (1991), no. 3, 157–165.
• [10] J. Vukman, A note on Jordan ∗-derivations in semiprime rings with involution, Int. Math. Forum 1 (2006), no. 13, 617–622, DOI: http://dx.doi.org/10.12988/imf.2006.06053.
• [11] S. Ali and A. Fošner, On Jordan ( )∗α β, -derivations in semiprime ∗-rings, Int. J. Algebra 4 (2010), no. 3, 99–108.
• [12] M. Ferrero and C. Haetinger, Higher derivations and a theorem by Herstein, Quaest. Math. 25 (2002), no. 2, 249–257, DOI: https://doi.org/10.2989/16073600209486012.
• [13] O. H. Ezzat, A note on Jordan triple higher ∗-derivations on semiprime rings, ISRN Algebra 2014 (2014), 1–5, DOI: https://doi.org/10.1155/2014/365424.