National Changhua University of Education Institutional Repository : Item 987654321/15019
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题名: Derivations Cocentralizing Multilinear Polynomials on Left Ideals
作者: Liu, Cheng-Kai
贡献者: 數學系
关键词: Derivation;PI;GPI;Prime ring;Differential identity
日期: 2011
上传时间: 2013-01-07T01:44:08Z
出版者: SpringerLink
摘要: Let R be a prime ring with extended centroid C, λ a nonzero left ideal of
R and f (X1, . . . , Xt ) a nonzero multilinear polynomial over C. Suppose that d and
δ are derivations of R such that
d( f (x1, . . . , xt )) f (x1, . . . , xt ) − f (x1, . . . , xt )δ( f (x1, . . . , xt )) ∈ C
for all x1, . . . , xt ∈ λ. Then either d = 0 and λδ(λ) = 0 or λC = RCe for some
idempotent e in the socle of RC and one of the following holds:
(1) f (X1, . . . , Xt ) is central-valued on eRCe;
(2) λ(d + δ)(λ) = 0 and f (X1, . . . , Xt )2 is central-valued on eRCe;
(3) char R = 2 and eRCe satisfies st4(X1, X2, X3, X4), the standard polynomial
identity of degree 4.
關聯: Monatshefte fur Mathematik, 162(3): 297-311
显示于类别:[數學系] 期刊論文

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