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Higher derivations of triangular algebras and its generalizations

✍ Scribed by Feng Wei; Zhankui Xiao

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
323 KB
Volume
435
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let R be a commutative ring with identity, A and B be unital algebras over R and M be a unital (A, B)-bimodule. Let T = A M 0 B be the triangular algebra consisting of A, B and M. Motivated by the work of Cheung [4] we mainly consider the question whether every higher derivation on a triangular algebra is an inner higher derivation. We also give some characterizations on (generalized-)Jordan (triple-)higher derivations of triangular algebras.

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✍ Peisheng Ji; Weiqing Qi πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 219 KB

Let T be a triangular algebra over a commutative ring R. In this paper, under some mild conditions on T , we prove that if for any x, y ∈ T with xy = 0 (resp. xy = p, where p is the standard idempotent of T ), then Ξ΄ = d + Ο„ , where d is a derivation of T and Ο„ : T -β†’ Z(T ) (where Z(T ) is the cent