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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.
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참고문헌 (16)
참고문헌 신청
D. Benkovic / 2012 / Jordan derivations of unital algebras with idempotents / Linear Algebra Appl 437(9):2271~2284
M. Bresar / 1989 / Jordan mappings of semiprime rings / J. Algebra 127(1):218~228
W. -S. Cheung / 2000 / Mappings on triangular algebras
H. Ghahramani / 2013 / Jordan derivations on trivial extensions / Bull. Iranian Math. Soc 39(4):635~645
I. N. Herstein / 1957 / Jordan derivations of prime rings / Proc. Amer. Math. Soc 8:1104~1110
M. Bresar / 1989 / Jordan mappings of semiprime rings / J. Algebra 127(1):218~228
W. -S. Cheung / 2000 / Mappings on triangular algebras
H. Ghahramani / 2013 / Jordan derivations on trivial extensions / Bull. Iranian Math. Soc 39(4):635~645
I. N. Herstein / 1957 / Jordan derivations of prime rings / Proc. Amer. Math. Soc 8:1104~1110
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