National Changhua University of Education Institutional Repository : Item 987654321/15019

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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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