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JORDAN HIGHER DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS
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 Title & Authors
JORDAN HIGHER DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS
Vishki, Hamid Reza Ebrahimi; Mirzavaziri, Madjid; Moafian, Fahimeh;
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 Abstract
We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.
 Keywords
higher derivation;Jordan higher derivation;trivial extension algebra;generalized matrix algebra;triangular algebra;
 Language
English
 Cited by
 References
1.
D. Benkovic and N. sirovnik, Jordan derivations of unital algebras with idempotents, Linear Algebra Appl. 437 (2012), no. 9, 2271-2284. crossref(new window)

2.
M. Bresar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), no. 1, 218-228. crossref(new window)

3.
W.-S. Cheung, Mappings on triangular algebras, Ph.D Thesis, University of Victoria, 2000.

4.
H. Ghahramani, Jordan derivations on trivial extensions, Bull. Iranian Math. Soc. 39 (2013), no. 4, 635-645.

5.
I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. crossref(new window)

6.
Y. Li, L. van Wyk and F. Wei, Jordan derivations and antiderivations of generalized matrix algebras, Oper. Matrices 7 (2013), no. 2, 399-415.

7.
M. Mirzavaziri, Characterization of higher derivations on algebras, Comm. Algebra 38 (2010), no. 3, 981-987. crossref(new window)

8.
F. Moafian, Higher derivations on trivial extension algebras and triangular algebras, Ph.D Thesis, Ferdowsi University of Mashhad, 2015.

9.
F. Moafian and H. R. Ebrahimi Vishki, Lie higher derivations on triangular algebras revisited, to appear in Filomat.

10.
A. H. Mokhtari, F. Moafian and H. R. Ebrahimi Vishki, Lie derivations on trivial extension algebras, arXiv:1504.05924v1 [math.RA].

11.
Y. Ohnuki, K. Takeda and K. Yamagata, Symmetric Hochschild extension algebras, Colloq. Math. 80 (1999), no. 2, 155-174.

12.
A. D. Sands, Radicals and Morita contexts, J. Algebra 24 (1973), 335-345. crossref(new window)

13.
Z. Xiao and F. Wei, Jordan higher derivations on triangular algebras, Linear Algebra Appl. 432 (2010), no. 10, 2615-2622. crossref(new window)

14.
Z. Xiao and F. Wei, Jordan higher derivations on some operator algebras, Houston J. Math. 38 (2012), no. 1, 275-293.

15.
J. H. Zhang and W. Y. Yu, Jordan derivations of triangular algebras, Linear Algebra Appl. 419 (2006), no. 1, 251-255. crossref(new window)

16.
Y. Zhang, Weak amenability of module extensions of Banach algebras, Trans. Amer. Math. Soc. 354 (2002), no. 10, 4131-4151. crossref(new window)