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 Title: Higher Derivations of Ore Extensions Authors: Chuang, Chen-Lian;Lee, Tsiu-Kwen;Liu, Cheng-Kai;Tsai, Yuan-Tsung Contributors: 數學系 Keywords: Derivation;Prime ring;Higher derivation;Bimodule map;Ore extension;Skew polynomial ring Date: 2010-01 Issue Date: 2013-01-07T01:44:06Z Publisher: SpringerLink Abstract: Let R be a prime ring and δ a derivation of R. Divided powers \$\$ D_n ^\underline\underline def. \tfrac1 n!\tfracd^n dx^n \$\$ of ordinary differentiation d/dx form Hasse-Schmidt higher derivations of the Ore extension (skew polynomial ring) R[x; δ]. They have been used crucially but implicitly in the investigation of R[x; δ]. Our aim is to explore this notion. The following is proved among others: Let Q be the left Martindale quotient ring of R. It is shown that \$\$ S^\underline\underline def. Q[x;δ ] \$\$ is a quasi-injective (R, R)-module and that any (R,R)-bimodule endomorphism of S can be uniquely expressed in the form \$\$ θ (f) = ∑\limits_n = 0^∞ ζ _n D_n (f) forf ∈ Q[x;δ ], \$\$ where ζ n ∈ C S (R), the centralizer of R in S. As an application, we also use the Ore extension R[x; δ] to deduce Kharchenko’s theorem for a single derivation. These results are extended to the Ore extension R[X;D] of R by a sequence D of derivations of R. Relation: Israel Journal of Mathematics, 175(1): 157-178 Appears in Collections: [數學系] 期刊論文

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