Generalized Derivations with Invertible or Nilpotent Values on Multilinear Polynomials |
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| Authors: | Jer-Shyong Lin Cheng-Kai Liu |
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| Institution: | 1. Department of Mathematics , National Tsing Hua University , Hsinchu, Taiwan jslin@math.nthu.edu.tw;3. Department of Mathematics , National Taiwan University , Taipei, Taiwan |
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| Abstract: | Let R be a ring with unity, g a generalized derivation on R and f(X 1,…,X k ) a multilinear polynomial. In this article we describe the structure of R provided that g(f(x 1,…,x k )) is either invertible or nilpotent for every x 1,…,x k in some nonzero ideal of R. |
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| Keywords: | Generalized derivation Multilinear polynomial Prime ring Semiprime ring |
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