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NCUEIR > College of Science > math > Periodical Articles >  Item 987654321/15019

Please use this identifier to cite or link to this item: http://ir.ncue.edu.tw/ir/handle/987654321/15019

Title: Derivations Cocentralizing Multilinear Polynomials on Left Ideals
Authors: Liu, Cheng-Kai
Contributors: 數學系
Keywords: Derivation;PI;GPI;Prime ring;Differential identity
Date: 2011
Issue Date: 2013-01-07T01:44:08Z
Publisher: SpringerLink
Abstract: 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.
Relation: Monatshefte fur Mathematik, 162(3): 297-311
Appears in Collections:[math] Periodical Articles

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